From 323867bc5bbfa20bd0d3144e3cfe8e331992b6c0 Mon Sep 17 00:00:00 2001 From: Pieter Wuille Date: Sat, 22 Dec 2018 01:27:14 -0800 Subject: [PATCH 1/2] Separate multiplier and nonzeromultiplier --- src/fields/clmul_common_impl.h | 2 ++ src/fields/generic_common_impl.h | 3 +++ src/sketch_impl.h | 11 ++++++----- 3 files changed, 11 insertions(+), 5 deletions(-) diff --git a/src/fields/clmul_common_impl.h b/src/fields/clmul_common_impl.h index 36f431a..d7fa8be 100644 --- a/src/fields/clmul_common_impl.h +++ b/src/fields/clmul_common_impl.h @@ -137,6 +137,8 @@ template #include +#include "../util.h" #include "../int_utils.h" #include "../lintrans.h" @@ -48,6 +49,8 @@ template(a.m_val)); } }; + typedef Multiplier NonZeroMultiplier; + inline friend constexpr Field operator+(Field a, Field b) { return Field(a.m_val ^ b.m_val); } inline Field& operator+=(Field a) { m_val ^= a.m_val; return *this; } friend Field operator*(Field a, Field b) { return Field(GFMul(a.m_val, b.m_val)); } diff --git a/src/sketch_impl.h b/src/sketch_impl.h index 4a87e17..f31ca02 100644 --- a/src/sketch_impl.h +++ b/src/sketch_impl.h @@ -24,7 +24,7 @@ void PolyMod(const std::vector& mod, std::vector& val) { F term = val.back(); val.pop_back(); if (!term.IsZero()) { - typename F::Multiplier mul(term); + typename F::NonZeroMultiplier mul(term); for (size_t x = 0; x < mod.size() - 1; ++x) { val[val.size() - modsize + 1 + x] += mul(mod[x]); } @@ -49,7 +49,7 @@ void DivMod(const std::vector& mod, std::vector& val, std::vector& div) div[val.size() - modsize] = term; val.pop_back(); if (!term.IsZero()) { - typename F::Multiplier mul(term); + typename F::NonZeroMultiplier mul(term); for (size_t x = 0; x < mod.size() - 1; ++x) { val[val.size() - modsize + 1 + x] += mul(mod[x]); } @@ -63,7 +63,7 @@ F MakeMonic(std::vector& a) { CHECK_SAFE(!a.back().IsZero()); if (a.back().IsOne()) return F::Zero(); auto inv = a.back().Inv(); - typename F::Multiplier mul(inv); + typename F::NonZeroMultiplier mul(inv); a.back() = F::One(); for (size_t i = 0; i < a.size() - 1; ++i) { a[i] = mul(a[i]); @@ -307,7 +307,7 @@ std::vector BerlekampMassey(const std::vector& syndromes, size_t max_degre tmp = current; current.resize(prev.size() + x); } - typename F::Multiplier mul(discrepancy * b_inv); + typename F::NonZeroMultiplier mul(discrepancy * b_inv); for (size_t i = 0; i < prev.size(); ++i) current[i + x] += mul(prev[i]); if (swap) { std::swap(prev, tmp); @@ -333,8 +333,9 @@ std::vector ReconstructAllSyndromes(const std::vector& odd_syndromes) { template void AddToOddSyndromes(std::vector& osyndromes, F data) { + if (data.IsZero()) return; auto sqr = data.Sqr(); - typename F::Multiplier mul(sqr); + typename F::NonZeroMultiplier mul(sqr); for (auto& osyndrome : osyndromes) { osyndrome += data; data = mul(data); From bd2906f658da64621382b36c7d61e13798e73ad5 Mon Sep 17 00:00:00 2001 From: Pieter Wuille Date: Tue, 25 Dec 2018 10:37:14 -0800 Subject: [PATCH 2/2] Add 'small' log/exp table based field implementations --- doc/gen_params.sage | 44 +++++++-- src/Makefile | 12 ++- src/fields/small.cpp | 221 +++++++++++++++++++++++++++++++++++++++++++ src/minisketch.cpp | 7 +- 4 files changed, 273 insertions(+), 11 deletions(-) create mode 100644 src/fields/small.cpp diff --git a/doc/gen_params.sage b/doc/gen_params.sage index afab497..5d6c0ac 100755 --- a/doc/gen_params.sage +++ b/doc/gen_params.sage @@ -128,8 +128,8 @@ def conv_tables(F, NF, bits): return (ret, ret2) def fmt(i,typ): - if i == 0: - return "0" + if i < 1000000000: + return "%i" % i else: return "0x%x" % i @@ -147,7 +147,8 @@ def lintranstype(typ, bits, maxtbl): INT=0 CLMUL=1 CLMUL_TRI=2 -MD=3 +SMALL=3 +MD=4 def print_modulus_md(mod): ret = "" @@ -169,7 +170,7 @@ def pick_modulus(bits, style): # Choose the lexicographicly-first lowest-weight modulus # optionally subject to implementation specific constraints. moduli = compute_moduli(bits) - if style == INT or style == MD: + if style == INT or style == SMALL or style == MD: multi_sqr = False need_trans = False elif style == CLMUL: @@ -194,19 +195,31 @@ def pick_modulus(bits, style): def print_result(bits, style): if style == INT: + log_table = False + single_sqr = True multi_sqr = False need_trans = False table_id = "%i" % bits elif style == MD: pass elif style == CLMUL: + log_table = False + single_sqr = True multi_sqr = True need_trans = True table_id = "%i" % bits elif style == CLMUL_TRI: + log_table = False + single_sqr = True multi_sqr = True need_trans = True table_id = "TRI%i" % bits + elif style == SMALL: + log_table = True + single_sqr = False + multi_sqr = False + need_trans = False + table_id = "%i" % bits else: assert(False) @@ -234,7 +247,7 @@ def print_result(bits, style): F. = GF(2**bits, modulus=modulus) include_table = True - if style != INT and style != CLMUL: + if style == CLMUL_TRI: cmodulus = pick_modulus(bits, CLMUL) if cmodulus == modulus: include_table = False @@ -266,7 +279,7 @@ def print_result(bits, style): else: assert(modulus == nmodulus) - if include_table: + if include_table and single_sqr: print("constexpr %s SQR_TABLE_%s({%s});" % (rtyp, table_id, ", ".join([fmt(x,typ) for x in sqr_table(f, bits, 1)]))) if multi_sqr: # Repeated squaring is a linearised polynomial so in F(2^n) it is @@ -296,6 +309,18 @@ def print_result(bits, style): if include_table: print("constexpr %s QRT_TABLE_%s({%s});" % (rtyp, table_id, ", ".join([fmt(x,typ) for x in qrt_table(F, f, bits)]))) + if log_table: + for baseval in range(2,2**bits): + try: + base = F.fetch_int(baseval) + logs = [2**bits-1] + [discrete_log(F.fetch_int(i), base) for i in range(1,2**bits)] + exps = [(base**i).integer_representation() for i in range(2**bits - 1)] + [1] + break + except: + continue + print("constexpr %s LOG_TABLE_%s[] = {%s};" % (typ, table_id, ", ".join([fmt(x,typ) for x in logs]))) + print("constexpr %s EXP_TABLE_%s[] = {%s};" % (typ, table_id, ", ".join([fmt(x,typ) for x in exps]))) + modulus_weight = modulus.hamming_weight() modulus_degree = (modulus - p**bits).degree() modulus_int = (modulus - p**bits).change_ring(ZZ)(2) @@ -304,6 +329,8 @@ def print_result(bits, style): if style == INT: print("typedef Field<%s, %i, %i, %s, %s, &SQR_TABLE_%s, &QRT_TABLE_%s%s> Field%i;" % (typ, bits, modulus_int, rtyp, ttyp, table_id, table_id, lfsr, bits)) + elif style == SMALL: + print("typedef Field<%s, %i, %i, LOG_TABLE_%s, EXP_TABLE_%s, %s, &QRT_TABLE_%s> Field%i;" % (typ, bits, modulus_int, table_id, table_id, rtyp, table_id, bits)) elif style == CLMUL: print("typedef Field<%s, %i, %i, %s, &SQR_TABLE_%s, %s, %s, %s, %s, &QRT_TABLE_%s, %s, %s, %s%s> Field%i;" % (typ, bits, modulus_int, rtyp, table_id, sqr2, sqr4, sqr8, sqr16, table_id, ctyp, loadtbl, savetbl, lfsr, bits)) elif style == CLMUL_TRI: @@ -311,6 +338,11 @@ def print_result(bits, style): else: assert(False) +for bits in range(2, 17): + print("// %i bit field" % bits) + print_result(bits, SMALL) + print("") + for bits in range(2, 65): print("// %i bit field" % bits) print_result(bits, INT) diff --git a/src/Makefile b/src/Makefile index 1fefd1d..2d78807 100644 --- a/src/Makefile +++ b/src/Makefile @@ -2,6 +2,8 @@ default: test-exhaust bench DEFINES := -DHAVE_CLZ -O2 -g0 +fields/small.o: fields/small.cpp lintrans.h sketch.h sketch_impl.h int_utils.h + $(CXX) $(DEFINES) -DNDEBUG -Wall -std=c++11 fields/small.cpp -c -o fields/small.o fields/generic_1byte.o: fields/generic_common_impl.h fields/generic_1byte.cpp lintrans.h sketch.h sketch_impl.h int_utils.h $(CXX) $(DEFINES) -DNDEBUG -Wall -std=c++11 fields/generic_1byte.cpp -c -o fields/generic_1byte.o fields/generic_2bytes.o: fields/generic_common_impl.h fields/generic_2bytes.cpp lintrans.h sketch.h sketch_impl.h int_utils.h @@ -37,6 +39,8 @@ fields/clmul_8bytes.o: fields/clmul_common_impl.h fields/clmul_8bytes.cpp lintra minisketch.o: minisketch.cpp ../include/minisketch.h $(CXX) $(DEFINES) -DNDEBUG -Wall -std=c++11 minisketch.cpp -c -o minisketch.o +fields/small_test.o: fields/small.cpp lintrans.h sketch.h sketch_impl.h int_utils.h + $(CXX) $(DEFINES) -DMINISKETCH_VERIFY -Wall -std=c++11 fields/small.cpp -c -o fields/small_test.o fields/generic_1byte_test.o: fields/generic_common_impl.h fields/generic_1byte.cpp lintrans.h sketch.h sketch_impl.h int_utils.h $(CXX) $(DEFINES) -DMINISKETCH_VERIFY -Wall -std=c++11 fields/generic_1byte.cpp -c -o fields/generic_1byte_test.o fields/generic_2bytes_test.o: fields/generic_common_impl.h fields/generic_2bytes.cpp lintrans.h sketch.h sketch_impl.h int_utils.h @@ -72,11 +76,11 @@ fields/clmul_8bytes_test.o: fields/clmul_common_impl.h fields/clmul_8bytes.cpp l minisketch_test.o: minisketch.cpp ../include/minisketch.h $(CXX) $(DEFINES) -DMINISKETCH_VERIFY -Wall -std=c++11 minisketch.cpp -c -o minisketch_test.o -libminisketch.a: fields/generic_1byte.o fields/generic_2bytes.o fields/generic_3bytes.o fields/generic_4bytes.o fields/generic_5bytes.o fields/generic_6bytes.o fields/generic_7bytes.o fields/generic_8bytes.o fields/clmul_1byte.o fields/clmul_2bytes.o fields/clmul_3bytes.o fields/clmul_4bytes.o fields/clmul_5bytes.o fields/clmul_6bytes.o fields/clmul_7bytes.o fields/clmul_8bytes.o minisketch.o - $(AR) cr libminisketch.a fields/generic_1byte.o fields/generic_2bytes.o fields/generic_3bytes.o fields/generic_4bytes.o fields/generic_5bytes.o fields/generic_6bytes.o fields/generic_7bytes.o fields/generic_8bytes.o fields/clmul_1byte.o fields/clmul_2bytes.o fields/clmul_3bytes.o fields/clmul_4bytes.o fields/clmul_5bytes.o fields/clmul_6bytes.o fields/clmul_7bytes.o fields/clmul_8bytes.o minisketch.o +libminisketch.a: fields/small.o fields/generic_1byte.o fields/generic_2bytes.o fields/generic_3bytes.o fields/generic_4bytes.o fields/generic_5bytes.o fields/generic_6bytes.o fields/generic_7bytes.o fields/generic_8bytes.o fields/clmul_1byte.o fields/clmul_2bytes.o fields/clmul_3bytes.o fields/clmul_4bytes.o fields/clmul_5bytes.o fields/clmul_6bytes.o fields/clmul_7bytes.o fields/clmul_8bytes.o minisketch.o + $(AR) cr libminisketch.a fields/small.o fields/generic_1byte.o fields/generic_2bytes.o fields/generic_3bytes.o fields/generic_4bytes.o fields/generic_5bytes.o fields/generic_6bytes.o fields/generic_7bytes.o fields/generic_8bytes.o fields/clmul_1byte.o fields/clmul_2bytes.o fields/clmul_3bytes.o fields/clmul_4bytes.o fields/clmul_5bytes.o fields/clmul_6bytes.o fields/clmul_7bytes.o fields/clmul_8bytes.o minisketch.o -libminisketch_test.a: fields/generic_1byte_test.o fields/generic_2bytes_test.o fields/generic_3bytes_test.o fields/generic_4bytes_test.o fields/generic_5bytes_test.o fields/generic_6bytes_test.o fields/generic_7bytes_test.o fields/generic_8bytes_test.o fields/clmul_1byte_test.o fields/clmul_2bytes_test.o fields/clmul_3bytes_test.o fields/clmul_4bytes_test.o fields/clmul_5bytes_test.o fields/clmul_6bytes_test.o fields/clmul_7bytes_test.o fields/clmul_8bytes_test.o minisketch_test.o - $(AR) cr libminisketch_test.a fields/generic_1byte_test.o fields/generic_2bytes_test.o fields/generic_3bytes_test.o fields/generic_4bytes_test.o fields/generic_5bytes_test.o fields/generic_6bytes_test.o fields/generic_7bytes_test.o fields/generic_8bytes_test.o fields/clmul_1byte_test.o fields/clmul_2bytes_test.o fields/clmul_3bytes_test.o fields/clmul_4bytes_test.o fields/clmul_5bytes_test.o fields/clmul_6bytes_test.o fields/clmul_7bytes_test.o fields/clmul_8bytes_test.o minisketch_test.o +libminisketch_test.a: fields/small_test.o fields/generic_1byte_test.o fields/generic_2bytes_test.o fields/generic_3bytes_test.o fields/generic_4bytes_test.o fields/generic_5bytes_test.o fields/generic_6bytes_test.o fields/generic_7bytes_test.o fields/generic_8bytes_test.o fields/clmul_1byte_test.o fields/clmul_2bytes_test.o fields/clmul_3bytes_test.o fields/clmul_4bytes_test.o fields/clmul_5bytes_test.o fields/clmul_6bytes_test.o fields/clmul_7bytes_test.o fields/clmul_8bytes_test.o minisketch_test.o + $(AR) cr libminisketch_test.a fields/small_test.o fields/generic_1byte_test.o fields/generic_2bytes_test.o fields/generic_3bytes_test.o fields/generic_4bytes_test.o fields/generic_5bytes_test.o fields/generic_6bytes_test.o fields/generic_7bytes_test.o fields/generic_8bytes_test.o fields/clmul_1byte_test.o fields/clmul_2bytes_test.o fields/clmul_3bytes_test.o fields/clmul_4bytes_test.o fields/clmul_5bytes_test.o fields/clmul_6bytes_test.o fields/clmul_7bytes_test.o fields/clmul_8bytes_test.o minisketch_test.o test-exhaust.o: test-exhaust.cpp ../include/minisketch.h $(CXX) $(DEFINES) -DMINISKETCH_VERIFY -Wall -std=c++11 test-exhaust.cpp -pthread -c -o test-exhaust.o diff --git a/src/fields/small.cpp b/src/fields/small.cpp new file mode 100644 index 0000000..69a32b6 --- /dev/null +++ b/src/fields/small.cpp @@ -0,0 +1,221 @@ +/********************************************************************** + * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko * + * Distributed under the MIT software license, see the accompanying * + * file LICENSE or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#include +#include + +#include "../util.h" +#include "../int_utils.h" +#include "../lintrans.h" +#include "../sketch_impl.h" + +namespace { + +/** Generic implementation for fields whose elements can be represented by an integer type. */ +template class Field +{ + typedef BitsInt O; + typedef LFSR L; + + I m_val; + explicit constexpr Field(I val) : m_val(val) {} + + constexpr inline static I Reduce(unsigned a) { return O::Mask(a + (a >> B)); } + +public: + static constexpr int BITS = B; + + static constexpr Field Zero() { return Field(I(0)); } + static constexpr Field One() { return Field(I(1)); } + + constexpr inline Field() : m_val(0) {} + constexpr inline bool IsZero() const { return m_val == 0; } + constexpr inline bool IsOne() const { return m_val == 1; } + + constexpr inline bool friend operator==(Field a, Field b) { return a.m_val == b.m_val; } + constexpr inline bool friend operator!=(Field a, Field b) { return a.m_val != b.m_val; } + constexpr inline bool friend operator<(Field a, Field b) { return a.m_val < b.m_val; } + + constexpr inline Field Mul2() const { return Field(L::Call(m_val)); } + + class Multiplier + { + int m_log; + public: + explicit Multiplier(Field a) : m_log(LOG[a.m_val]) {} + constexpr inline Field operator()(Field a) const { return Field((m_log == (1 << B) - 1 || a.m_val == 0) ? 0 : EXP[Reduce(LOG[a.m_val] + m_log)]); } + }; + + class NonZeroMultiplier + { + int m_log; + public: + explicit NonZeroMultiplier(Field a) : m_log(LOG[a.m_val]) { CHECK(!a.IsZero()); } + constexpr inline Field operator()(Field a) const { return Field(a.m_val == 0 ? 0 : EXP[Reduce(LOG[a.m_val] + m_log)]); } + }; + + inline friend constexpr Field operator+(Field a, Field b) { return Field(a.m_val ^ b.m_val); } + inline Field& operator+=(Field a) { m_val ^= a.m_val; return *this; } + friend Field operator*(Field a, Field b) { return Field(GFMul(a.m_val, b.m_val)); } + + /** Compute the square of a. */ + inline constexpr Field Sqr() const { return Field(m_val == 0 ? 0 : EXP[Reduce(LOG[m_val] * 2)]); } + + /** Compute x such that x^2 + x = a (undefined result if no solution exists). */ + inline constexpr Field Qrt() const { return Field(QRT->template Map(m_val)); } + + /** Compute the inverse of x1. */ + inline constexpr Field Inv() { return Field(m_val == 0 ? 0 : EXP[(1 << B) - 1 - LOG[m_val]]); } + + /** Generate a random field element. */ + static Field FromSeed(uint64_t seed) { + uint64_t k0 = 0x496e744669656c64ull; // "IntField" + uint64_t k1 = seed; + uint64_t count = ((uint64_t)BITS) << 32; + I ret; + do { + ret = O::Mask(I(SipHash(k0, k1, count++))); + } while(ret == 0); + return Field(ret); + } + + static Field Deserialize(BitReader& in) { return Field(in.template Read()); } + + void Serialize(BitWriter& out) const { out.template Write(m_val); } + + static constexpr Field FromUint64(uint64_t x) { return Field(O::Mask(I(x))); } + constexpr uint64_t ToUint64() const { return uint64_t(m_val); } +}; + +// 2 bit field +typedef RecLinTrans StatTable2; +constexpr StatTable2 QRT_TABLE_2({2, 0}); +constexpr uint8_t LOG_TABLE_2[] = {3, 0, 1, 2}; +constexpr uint8_t EXP_TABLE_2[] = {1, 2, 3, 1}; +typedef Field Field2; + +// 3 bit field +typedef RecLinTrans StatTable3; +constexpr StatTable3 QRT_TABLE_3({0, 4, 6}); +constexpr uint8_t LOG_TABLE_3[] = {7, 0, 1, 3, 2, 6, 4, 5}; +constexpr uint8_t EXP_TABLE_3[] = {1, 2, 4, 3, 6, 7, 5, 1}; +typedef Field Field3; + +// 4 bit field +typedef RecLinTrans StatTable4; +constexpr StatTable4 QRT_TABLE_4({6, 10, 8, 0}); +constexpr uint8_t LOG_TABLE_4[] = {15, 0, 1, 4, 2, 8, 5, 10, 3, 14, 9, 7, 6, 13, 11, 12}; +constexpr uint8_t EXP_TABLE_4[] = {1, 2, 4, 8, 3, 6, 12, 11, 5, 10, 7, 14, 15, 13, 9, 1}; +typedef Field Field4; + +// 5 bit field +typedef RecLinTrans StatTable5; +constexpr StatTable5 QRT_TABLE_5({20, 8, 10, 0, 14}); +constexpr uint8_t LOG_TABLE_5[] = {31, 0, 1, 18, 2, 5, 19, 11, 3, 29, 6, 27, 20, 8, 12, 23, 4, 10, 30, 17, 7, 22, 28, 26, 21, 25, 9, 16, 13, 14, 24, 15}; +constexpr uint8_t EXP_TABLE_5[] = {1, 2, 4, 8, 16, 5, 10, 20, 13, 26, 17, 7, 14, 28, 29, 31, 27, 19, 3, 6, 12, 24, 21, 15, 30, 25, 23, 11, 22, 9, 18, 1}; +typedef Field Field5; + +// 6 bit field +typedef RecLinTrans StatTable6; +constexpr StatTable6 QRT_TABLE_6({58, 38, 36, 20, 32, 0}); +constexpr uint8_t LOG_TABLE_6[] = {63, 0, 1, 6, 2, 12, 7, 26, 3, 32, 13, 35, 8, 48, 27, 18, 4, 24, 33, 16, 14, 52, 36, 54, 9, 45, 49, 38, 28, 41, 19, 56, 5, 62, 25, 11, 34, 31, 17, 47, 15, 23, 53, 51, 37, 44, 55, 40, 10, 61, 46, 30, 50, 22, 39, 43, 29, 60, 42, 21, 20, 59, 57, 58}; +constexpr uint8_t EXP_TABLE_6[] = {1, 2, 4, 8, 16, 32, 3, 6, 12, 24, 48, 35, 5, 10, 20, 40, 19, 38, 15, 30, 60, 59, 53, 41, 17, 34, 7, 14, 28, 56, 51, 37, 9, 18, 36, 11, 22, 44, 27, 54, 47, 29, 58, 55, 45, 25, 50, 39, 13, 26, 52, 43, 21, 42, 23, 46, 31, 62, 63, 61, 57, 49, 33, 1}; +typedef Field Field6; + +// 7 bit field +typedef RecLinTrans StatTable7; +constexpr StatTable7 QRT_TABLE_7({0, 20, 22, 114, 18, 64, 122}); +constexpr uint8_t LOG_TABLE_7[] = {127, 0, 1, 7, 2, 14, 8, 56, 3, 63, 15, 31, 9, 90, 57, 21, 4, 28, 64, 67, 16, 112, 32, 97, 10, 108, 91, 70, 58, 38, 22, 47, 5, 54, 29, 19, 65, 95, 68, 45, 17, 43, 113, 115, 33, 77, 98, 117, 11, 87, 109, 35, 92, 74, 71, 79, 59, 104, 39, 100, 23, 82, 48, 119, 6, 126, 55, 13, 30, 62, 20, 89, 66, 27, 96, 111, 69, 107, 46, 37, 18, 53, 44, 94, 114, 42, 116, 76, 34, 86, 78, 73, 99, 103, 118, 81, 12, 125, 88, 61, 110, 26, 36, 106, 93, 52, 75, 41, 72, 85, 80, 102, 60, 124, 105, 25, 40, 51, 101, 84, 24, 123, 83, 50, 49, 122, 120, 121}; +constexpr uint8_t EXP_TABLE_7[] = {1, 2, 4, 8, 16, 32, 64, 3, 6, 12, 24, 48, 96, 67, 5, 10, 20, 40, 80, 35, 70, 15, 30, 60, 120, 115, 101, 73, 17, 34, 68, 11, 22, 44, 88, 51, 102, 79, 29, 58, 116, 107, 85, 41, 82, 39, 78, 31, 62, 124, 123, 117, 105, 81, 33, 66, 7, 14, 28, 56, 112, 99, 69, 9, 18, 36, 72, 19, 38, 76, 27, 54, 108, 91, 53, 106, 87, 45, 90, 55, 110, 95, 61, 122, 119, 109, 89, 49, 98, 71, 13, 26, 52, 104, 83, 37, 74, 23, 46, 92, 59, 118, 111, 93, 57, 114, 103, 77, 25, 50, 100, 75, 21, 42, 84, 43, 86, 47, 94, 63, 126, 127, 125, 121, 113, 97, 65, 1}; +typedef Field Field7; + +// 8 bit field +typedef RecLinTrans StatTable8; +constexpr StatTable8 QRT_TABLE_8({188, 42, 40, 134, 44, 222, 142, 0}); +constexpr uint8_t LOG_TABLE_8[] = {255, 0, 25, 1, 50, 2, 26, 198, 75, 199, 27, 104, 51, 238, 223, 3, 100, 4, 224, 14, 52, 141, 129, 239, 76, 113, 8, 200, 248, 105, 28, 193, 125, 194, 29, 181, 249, 185, 39, 106, 77, 228, 166, 114, 154, 201, 9, 120, 101, 47, 138, 5, 33, 15, 225, 36, 18, 240, 130, 69, 53, 147, 218, 142, 150, 143, 219, 189, 54, 208, 206, 148, 19, 92, 210, 241, 64, 70, 131, 56, 102, 221, 253, 48, 191, 6, 139, 98, 179, 37, 226, 152, 34, 136, 145, 16, 126, 110, 72, 195, 163, 182, 30, 66, 58, 107, 40, 84, 250, 133, 61, 186, 43, 121, 10, 21, 155, 159, 94, 202, 78, 212, 172, 229, 243, 115, 167, 87, 175, 88, 168, 80, 244, 234, 214, 116, 79, 174, 233, 213, 231, 230, 173, 232, 44, 215, 117, 122, 235, 22, 11, 245, 89, 203, 95, 176, 156, 169, 81, 160, 127, 12, 246, 111, 23, 196, 73, 236, 216, 67, 31, 45, 164, 118, 123, 183, 204, 187, 62, 90, 251, 96, 177, 134, 59, 82, 161, 108, 170, 85, 41, 157, 151, 178, 135, 144, 97, 190, 220, 252, 188, 149, 207, 205, 55, 63, 91, 209, 83, 57, 132, 60, 65, 162, 109, 71, 20, 42, 158, 93, 86, 242, 211, 171, 68, 17, 146, 217, 35, 32, 46, 137, 180, 124, 184, 38, 119, 153, 227, 165, 103, 74, 237, 222, 197, 49, 254, 24, 13, 99, 140, 128, 192, 247, 112, 7}; +constexpr uint8_t EXP_TABLE_8[] = {1, 3, 5, 15, 17, 51, 85, 255, 26, 46, 114, 150, 161, 248, 19, 53, 95, 225, 56, 72, 216, 115, 149, 164, 247, 2, 6, 10, 30, 34, 102, 170, 229, 52, 92, 228, 55, 89, 235, 38, 106, 190, 217, 112, 144, 171, 230, 49, 83, 245, 4, 12, 20, 60, 68, 204, 79, 209, 104, 184, 211, 110, 178, 205, 76, 212, 103, 169, 224, 59, 77, 215, 98, 166, 241, 8, 24, 40, 120, 136, 131, 158, 185, 208, 107, 189, 220, 127, 129, 152, 179, 206, 73, 219, 118, 154, 181, 196, 87, 249, 16, 48, 80, 240, 11, 29, 39, 105, 187, 214, 97, 163, 254, 25, 43, 125, 135, 146, 173, 236, 47, 113, 147, 174, 233, 32, 96, 160, 251, 22, 58, 78, 210, 109, 183, 194, 93, 231, 50, 86, 250, 21, 63, 65, 195, 94, 226, 61, 71, 201, 64, 192, 91, 237, 44, 116, 156, 191, 218, 117, 159, 186, 213, 100, 172, 239, 42, 126, 130, 157, 188, 223, 122, 142, 137, 128, 155, 182, 193, 88, 232, 35, 101, 175, 234, 37, 111, 177, 200, 67, 197, 84, 252, 31, 33, 99, 165, 244, 7, 9, 27, 45, 119, 153, 176, 203, 70, 202, 69, 207, 74, 222, 121, 139, 134, 145, 168, 227, 62, 66, 198, 81, 243, 14, 18, 54, 90, 238, 41, 123, 141, 140, 143, 138, 133, 148, 167, 242, 13, 23, 57, 75, 221, 124, 132, 151, 162, 253, 28, 36, 108, 180, 199, 82, 246, 1}; +typedef Field Field8; + +// 9 bit field +typedef RecLinTrans StatTable9; +constexpr StatTable9 QRT_TABLE_9({0, 78, 76, 426, 72, 34, 418, 256, 88}); +constexpr uint16_t LOG_TABLE_9[] = {511, 0, 252, 224, 504, 448, 476, 1, 245, 225, 189, 184, 217, 111, 253, 161, 497, 385, 477, 242, 441, 2, 436, 335, 469, 389, 363, 449, 505, 408, 413, 32, 238, 256, 126, 112, 218, 423, 494, 121, 182, 411, 254, 102, 177, 162, 76, 460, 210, 185, 130, 98, 104, 466, 190, 341, 246, 48, 149, 45, 154, 87, 284, 226, 490, 450, 508, 204, 378, 368, 364, 311, 470, 27, 164, 272, 235, 269, 373, 390, 434, 222, 152, 409, 506, 322, 354, 324, 429, 54, 414, 6, 328, 33, 201, 179, 462, 16, 437, 480, 382, 336, 350, 92, 356, 345, 207, 3, 442, 195, 82, 136, 498, 173, 300, 107, 401, 78, 297, 386, 406, 243, 339, 124, 25, 326, 478, 295, 231, 8, 191, 168, 249, 342, 456, 39, 119, 128, 109, 467, 105, 348, 52, 233, 211, 318, 279, 397, 416, 331, 13, 186, 487, 99, 10, 143, 114, 393, 131, 302, 175, 46, 474, 240, 404, 193, 150, 309, 247, 316, 63, 56, 95, 426, 65, 49, 170, 360, 306, 88, 155, 500, 258, 419, 69, 264, 285, 58, 453, 227, 431, 42, 203, 377, 268, 163, 178, 428, 221, 353, 123, 24, 77, 299, 91, 461, 344, 81, 97, 103, 86, 148, 459, 181, 255, 493, 183, 216, 447, 251, 334, 496, 388, 412, 239, 403, 425, 62, 41, 68, 359, 257, 142, 113, 330, 278, 38, 230, 127, 51, 147, 458, 495, 446, 80, 122, 376, 220, 277, 37, 67, 424, 219, 146, 36, 35, 483, 259, 260, 196, 443, 484, 420, 370, 501, 133, 83, 261, 197, 137, 291, 156, 371, 4, 380, 171, 361, 159, 208, 421, 357, 444, 89, 214, 304, 307, 485, 346, 463, 198, 59, 116, 20, 286, 138, 17, 157, 481, 72, 70, 265, 313, 438, 292, 228, 275, 351, 84, 262, 93, 395, 454, 366, 432, 134, 337, 383, 502, 43, 74, 427, 267, 298, 90, 215, 387, 492, 96, 145, 66, 445, 79, 402, 358, 50, 141, 499, 305, 57, 452, 315, 64, 308, 174, 347, 108, 167, 248, 317, 12, 301, 486, 422, 125, 101, 176, 47, 283, 340, 209, 407, 362, 241, 440, 510, 475, 160, 244, 321, 151, 5, 327, 26, 372, 310, 489, 194, 206, 479, 381, 172, 296, 294, 405, 455, 7, 118, 232, 9, 392, 415, 396, 430, 263, 169, 418, 473, 192, 94, 55, 375, 457, 276, 34, 329, 229, 40, 61, 343, 23, 202, 352, 85, 180, 333, 250, 349, 15, 355, 135, 338, 325, 400, 106, 200, 53, 433, 323, 507, 367, 234, 271, 435, 384, 468, 31, 188, 110, 503, 223, 75, 410, 237, 120, 129, 465, 153, 44, 491, 266, 144, 140, 166, 11, 314, 451, 293, 205, 320, 488, 100, 282, 509, 439, 394, 274, 365, 73, 71, 312, 19, 115, 290, 132, 482, 369, 379, 158, 303, 213, 399, 14, 199, 270, 236, 464, 187, 30, 332, 22, 374, 60, 117, 391, 472, 417, 18, 273, 289, 212, 319, 281, 165, 139, 471, 21, 398, 29, 288, 280, 287, 28}; +constexpr uint16_t EXP_TABLE_9[] = {1, 7, 21, 107, 273, 370, 91, 385, 129, 388, 154, 453, 349, 150, 481, 417, 97, 295, 496, 470, 292, 505, 489, 409, 201, 124, 372, 73, 511, 507, 487, 435, 31, 93, 403, 255, 254, 249, 236, 135, 406, 228, 191, 318, 447, 59, 161, 356, 57, 175, 334, 239, 142, 425, 89, 399, 171, 338, 187, 290, 491, 407, 227, 170, 341, 174, 329, 250, 229, 184, 299, 468, 298, 467, 319, 440, 46, 202, 117, 331, 244, 207, 110, 266, 307, 412, 210, 61, 179, 282, 323, 204, 103, 309, 398, 172, 327, 208, 51, 153, 460, 354, 43, 209, 52, 140, 423, 115, 345, 138, 437, 13, 35, 233, 156, 471, 291, 492, 386, 136, 443, 39, 245, 200, 123, 353, 34, 238, 137, 444, 50, 158, 473, 265, 314, 419, 111, 269, 294, 503, 451, 335, 232, 155, 450, 328, 253, 240, 211, 58, 166, 369, 82, 446, 60, 180, 271, 296, 477, 277, 366, 15, 45, 195, 74, 502, 452, 346, 131, 394, 176, 275, 380, 113, 343, 160, 355, 44, 196, 95, 413, 213, 40, 216, 11, 49, 151, 486, 436, 10, 54, 130, 397, 165, 376, 109, 259, 268, 289, 482, 424, 94, 410, 192, 67, 457, 377, 106, 278, 359, 48, 144, 499, 479, 283, 324, 217, 12, 36, 252, 247, 198, 81, 439, 3, 9, 63, 189, 304, 405, 237, 128, 387, 143, 430, 76, 484, 442, 32, 224, 163, 362, 19, 121, 367, 8, 56, 168, 347, 132, 415, 219, 2, 14, 42, 214, 33, 231, 182, 257, 258, 267, 308, 393, 185, 300, 449, 321, 194, 77, 483, 431, 75, 497, 465, 305, 402, 248, 235, 146, 509, 501, 461, 357, 62, 186, 293, 510, 508, 498, 472, 270, 303, 456, 382, 127, 381, 118, 322, 203, 114, 350, 159, 478, 284, 337, 178, 285, 342, 167, 374, 71, 469, 301, 454, 340, 169, 348, 145, 500, 458, 368, 85, 427, 87, 421, 125, 371, 92, 404, 234, 149, 488, 414, 220, 23, 101, 315, 420, 122, 358, 55, 133, 408, 206, 105, 287, 344, 141, 416, 102, 306, 411, 199, 86, 418, 104, 280, 333, 230, 177, 276, 361, 26, 70, 466, 312, 429, 69, 475, 263, 272, 373, 78, 490, 400, 246, 193, 68, 476, 274, 379, 100, 316, 433, 17, 119, 325, 222, 25, 79, 493, 389, 157, 464, 310, 391, 147, 506, 480, 422, 116, 332, 225, 164, 383, 120, 360, 29, 83, 441, 41, 223, 30, 90, 390, 148, 495, 395, 183, 262, 279, 352, 37, 251, 226, 173, 320, 197, 88, 392, 190, 313, 426, 80, 432, 22, 98, 302, 463, 363, 20, 108, 260, 281, 330, 243, 218, 5, 27, 65, 455, 339, 188, 311, 384, 134, 401, 241, 212, 47, 205, 96, 288, 485, 445, 53, 139, 434, 24, 72, 504, 494, 396, 162, 365, 6, 18, 126, 378, 99, 297, 474, 256, 261, 286, 351, 152, 459, 375, 64, 448, 326, 215, 38, 242, 221, 16, 112, 336, 181, 264, 317, 438, 4, 28, 84, 428, 66, 462, 364, 1}; +typedef Field Field9; + +// 10 bit field +typedef RecLinTrans StatTable10; +constexpr StatTable10 QRT_TABLE_10({236, 134, 132, 782, 128, 962, 774, 0, 144, 662}); +constexpr uint16_t LOG_TABLE_10[] = {1023, 0, 1, 77, 2, 154, 78, 956, 3, 10, 155, 325, 79, 618, 957, 231, 4, 308, 11, 200, 156, 889, 326, 695, 80, 24, 619, 87, 958, 402, 232, 436, 5, 513, 309, 551, 12, 40, 201, 479, 157, 518, 890, 101, 327, 164, 696, 860, 81, 258, 25, 385, 620, 277, 88, 577, 959, 772, 403, 680, 233, 52, 437, 966, 6, 20, 514, 768, 310, 650, 552, 129, 13, 314, 41, 849, 202, 757, 480, 980, 158, 213, 519, 335, 891, 462, 102, 907, 328, 654, 165, 264, 697, 369, 861, 354, 82, 675, 259, 590, 26, 628, 386, 991, 621, 556, 278, 822, 89, 219, 578, 117, 960, 937, 773, 533, 404, 491, 681, 241, 234, 133, 53, 595, 438, 178, 967, 943, 7, 1020, 21, 305, 515, 510, 769, 255, 311, 17, 651, 210, 553, 672, 130, 934, 14, 1017, 315, 1014, 42, 610, 850, 191, 203, 318, 758, 31, 481, 428, 981, 568, 159, 613, 214, 752, 520, 667, 336, 788, 892, 45, 463, 801, 103, 525, 908, 705, 329, 194, 655, 1008, 166, 642, 265, 296, 698, 853, 370, 633, 862, 899, 355, 779, 83, 321, 676, 97, 260, 845, 591, 818, 27, 206, 629, 797, 387, 793, 992, 727, 622, 34, 557, 661, 279, 420, 823, 834, 90, 761, 220, 391, 579, 926, 118, 451, 961, 431, 938, 349, 774, 563, 534, 446, 405, 484, 492, 731, 682, 341, 242, 714, 235, 571, 134, 290, 54, 412, 596, 140, 439, 984, 179, 996, 968, 810, 944, 539, 8, 616, 1021, 152, 22, 400, 306, 887, 516, 162, 511, 38, 770, 50, 256, 275, 312, 755, 18, 648, 652, 367, 211, 460, 554, 217, 673, 626, 131, 176, 935, 489, 15, 670, 1018, 508, 316, 426, 1015, 608, 43, 523, 611, 665, 851, 897, 192, 640, 204, 791, 319, 843, 759, 924, 32, 418, 482, 339, 429, 561, 982, 808, 569, 410, 160, 48, 614, 398, 215, 174, 753, 365, 521, 895, 668, 424, 337, 806, 789, 922, 893, 804, 46, 172, 464, 872, 802, 870, 104, 466, 526, 283, 909, 874, 706, 736, 330, 528, 195, 380, 656, 285, 1009, 1003, 167, 106, 643, 838, 266, 468, 297, 66, 699, 708, 854, 111, 371, 738, 634, 60, 863, 911, 900, 827, 356, 876, 780, 497, 84, 197, 322, 74, 677, 382, 98, 548, 261, 332, 846, 765, 592, 530, 819, 587, 28, 1011, 207, 302, 630, 1005, 798, 749, 388, 658, 794, 94, 993, 287, 728, 346, 623, 645, 35, 149, 558, 840, 662, 505, 280, 169, 421, 395, 824, 108, 835, 377, 91, 299, 762, 71, 221, 68, 392, 146, 580, 268, 927, 224, 119, 470, 452, 687, 962, 856, 432, 227, 939, 113, 350, 976, 775, 701, 564, 930, 535, 710, 447, 723, 406, 636, 485, 271, 493, 62, 732, 918, 683, 373, 342, 583, 243, 740, 715, 719, 236, 902, 572, 690, 135, 829, 291, 186, 55, 865, 413, 455, 597, 913, 141, 744, 440, 782, 985, 473, 180, 499, 997, 602, 969, 358, 811, 122, 945, 878, 540, 247, 9, 324, 617, 230, 1022, 76, 153, 955, 23, 86, 401, 435, 307, 199, 888, 694, 517, 100, 163, 859, 512, 550, 39, 478, 771, 679, 51, 965, 257, 384, 276, 576, 313, 848, 756, 979, 19, 767, 649, 128, 653, 263, 368, 353, 212, 334, 461, 906, 555, 821, 218, 116, 674, 589, 627, 990, 132, 594, 177, 942, 936, 532, 490, 240, 16, 209, 671, 933, 1019, 304, 509, 254, 317, 30, 427, 567, 1016, 1013, 609, 190, 44, 800, 524, 704, 612, 751, 666, 787, 852, 632, 898, 778, 193, 1007, 641, 295, 205, 796, 792, 726, 320, 96, 844, 817, 760, 390, 925, 450, 33, 660, 419, 833, 483, 730, 340, 713, 430, 348, 562, 445, 983, 995, 809, 538, 570, 289, 411, 139, 161, 37, 49, 274, 615, 151, 399, 886, 216, 625, 175, 488, 754, 647, 366, 459, 522, 664, 896, 639, 669, 507, 425, 607, 338, 560, 807, 409, 790, 842, 923, 417, 894, 423, 805, 921, 47, 397, 173, 364, 465, 282, 873, 735, 803, 171, 871, 869, 105, 837, 467, 65, 527, 379, 284, 1002, 910, 826, 875, 496, 707, 110, 737, 59, 331, 764, 529, 586, 196, 73, 381, 547, 657, 93, 286, 345, 1010, 301, 1004, 748, 168, 394, 107, 376, 644, 148, 839, 504, 267, 223, 469, 686, 298, 70, 67, 145, 700, 929, 709, 722, 855, 226, 112, 975, 372, 582, 739, 718, 635, 270, 61, 917, 864, 454, 912, 743, 901, 689, 828, 185, 357, 121, 877, 246, 781, 472, 498, 601, 85, 434, 198, 693, 323, 229, 75, 954, 678, 964, 383, 575, 99, 858, 549, 477, 262, 352, 333, 905, 847, 978, 766, 127, 593, 941, 531, 239, 820, 115, 588, 989, 29, 566, 1012, 189, 208, 932, 303, 253, 631, 777, 1006, 294, 799, 703, 750, 786, 389, 449, 659, 832, 795, 725, 95, 816, 994, 537, 288, 138, 729, 712, 347, 444, 624, 487, 646, 458, 36, 273, 150, 885, 559, 408, 841, 416, 663, 638, 506, 606, 281, 734, 170, 868, 422, 920, 396, 363, 825, 495, 109, 58, 836, 64, 378, 1001, 92, 344, 300, 747, 763, 585, 72, 546, 222, 685, 69, 144, 393, 375, 147, 503, 581, 717, 269, 916, 928, 721, 225, 974, 120, 245, 471, 600, 453, 742, 688, 184, 963, 574, 857, 476, 433, 692, 228, 953, 940, 238, 114, 988, 351, 904, 977, 126, 776, 293, 702, 785, 565, 188, 931, 252, 536, 137, 711, 443, 448, 831, 724, 815, 407, 415, 637, 605, 486, 457, 272, 884, 494, 57, 63, 1000, 733, 867, 919, 362, 684, 143, 374, 502, 343, 746, 584, 545, 244, 599, 741, 183, 716, 915, 720, 973, 237, 987, 903, 125, 573, 475, 691, 952, 136, 442, 830, 814, 292, 784, 187, 251, 56, 999, 866, 361, 414, 604, 456, 883, 598, 182, 914, 972, 142, 501, 745, 544, 441, 813, 783, 250, 986, 124, 474, 951, 181, 971, 500, 543, 998, 360, 603, 882, 970, 542, 359, 881, 812, 249, 123, 950, 946, 947, 879, 948, 541, 880, 248, 949}; +constexpr uint16_t EXP_TABLE_10[] = {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 9, 18, 36, 72, 144, 288, 576, 137, 274, 548, 65, 130, 260, 520, 25, 50, 100, 200, 400, 800, 585, 155, 310, 620, 209, 418, 836, 641, 267, 534, 37, 74, 148, 296, 592, 169, 338, 676, 321, 642, 269, 538, 61, 122, 244, 488, 976, 937, 859, 703, 375, 750, 469, 938, 861, 691, 367, 734, 437, 874, 733, 435, 870, 709, 387, 774, 517, 3, 6, 12, 24, 48, 96, 192, 384, 768, 521, 27, 54, 108, 216, 432, 864, 713, 411, 822, 613, 195, 390, 780, 529, 43, 86, 172, 344, 688, 361, 722, 429, 858, 701, 371, 742, 453, 906, 797, 563, 111, 222, 444, 888, 761, 507, 1014, 997, 963, 911, 791, 551, 71, 142, 284, 568, 121, 242, 484, 968, 921, 827, 639, 247, 494, 988, 945, 875, 735, 439, 878, 725, 419, 838, 645, 259, 518, 5, 10, 20, 40, 80, 160, 320, 640, 265, 530, 45, 90, 180, 360, 720, 425, 850, 685, 339, 678, 325, 650, 285, 570, 125, 250, 500, 1000, 985, 955, 895, 759, 487, 974, 917, 803, 591, 151, 302, 604, 177, 354, 708, 385, 770, 525, 19, 38, 76, 152, 304, 608, 201, 402, 804, 577, 139, 278, 556, 81, 162, 324, 648, 281, 562, 109, 218, 436, 872, 729, 443, 886, 741, 451, 902, 773, 515, 15, 30, 60, 120, 240, 480, 960, 905, 795, 575, 119, 238, 476, 952, 889, 763, 511, 1022, 1013, 995, 975, 919, 807, 583, 135, 270, 540, 49, 98, 196, 392, 784, 553, 91, 182, 364, 728, 441, 882, 749, 467, 934, 837, 643, 271, 542, 53, 106, 212, 424, 848, 681, 347, 694, 357, 714, 413, 826, 637, 243, 486, 972, 913, 811, 607, 183, 366, 732, 433, 866, 717, 403, 806, 581, 131, 262, 524, 17, 34, 68, 136, 272, 544, 73, 146, 292, 584, 153, 306, 612, 193, 386, 772, 513, 11, 22, 44, 88, 176, 352, 704, 393, 786, 557, 83, 166, 332, 664, 313, 626, 237, 474, 948, 865, 715, 415, 830, 629, 227, 454, 908, 785, 555, 95, 190, 380, 760, 505, 1010, 1005, 979, 943, 855, 679, 327, 654, 277, 554, 93, 186, 372, 744, 473, 946, 877, 723, 431, 862, 693, 355, 710, 389, 778, 541, 51, 102, 204, 408, 816, 617, 219, 438, 876, 721, 427, 854, 677, 323, 646, 261, 522, 29, 58, 116, 232, 464, 928, 841, 667, 319, 638, 245, 490, 980, 929, 843, 671, 311, 622, 213, 426, 852, 673, 331, 662, 293, 586, 157, 314, 628, 225, 450, 900, 769, 523, 31, 62, 124, 248, 496, 992, 969, 923, 831, 631, 231, 462, 924, 817, 619, 223, 446, 892, 753, 491, 982, 933, 835, 655, 279, 558, 85, 170, 340, 680, 345, 690, 365, 730, 445, 890, 765, 499, 998, 965, 899, 783, 535, 39, 78, 156, 312, 624, 233, 466, 932, 833, 651, 287, 574, 117, 234, 468, 936, 857, 699, 383, 766, 501, 1002, 989, 947, 879, 727, 423, 846, 661, 291, 582, 133, 266, 532, 33, 66, 132, 264, 528, 41, 82, 164, 328, 656, 297, 594, 173, 346, 692, 353, 706, 397, 794, 573, 115, 230, 460, 920, 825, 635, 255, 510, 1020, 1009, 1003, 991, 951, 871, 711, 391, 782, 533, 35, 70, 140, 280, 560, 105, 210, 420, 840, 665, 315, 630, 229, 458, 916, 801, 587, 159, 318, 636, 241, 482, 964, 897, 779, 543, 55, 110, 220, 440, 880, 745, 475, 950, 869, 707, 399, 798, 565, 99, 198, 396, 792, 569, 123, 246, 492, 984, 953, 891, 767, 503, 1006, 981, 931, 847, 663, 295, 590, 149, 298, 596, 161, 322, 644, 257, 514, 13, 26, 52, 104, 208, 416, 832, 649, 283, 566, 101, 202, 404, 808, 601, 187, 374, 748, 465, 930, 845, 659, 303, 606, 181, 362, 724, 417, 834, 653, 275, 550, 69, 138, 276, 552, 89, 178, 356, 712, 409, 818, 621, 211, 422, 844, 657, 299, 598, 165, 330, 660, 289, 578, 141, 282, 564, 97, 194, 388, 776, 537, 59, 118, 236, 472, 944, 873, 731, 447, 894, 757, 483, 966, 901, 771, 527, 23, 46, 92, 184, 368, 736, 457, 914, 813, 595, 175, 350, 700, 369, 738, 461, 922, 829, 627, 239, 478, 956, 881, 747, 479, 958, 885, 739, 463, 926, 821, 611, 207, 414, 828, 625, 235, 470, 940, 849, 683, 351, 702, 373, 746, 477, 954, 893, 755, 495, 990, 949, 867, 719, 407, 814, 597, 163, 326, 652, 273, 546, 77, 154, 308, 616, 217, 434, 868, 705, 395, 790, 549, 67, 134, 268, 536, 57, 114, 228, 456, 912, 809, 603, 191, 382, 764, 497, 994, 973, 915, 815, 599, 167, 334, 668, 305, 610, 205, 410, 820, 609, 203, 406, 812, 593, 171, 342, 684, 337, 674, 333, 666, 317, 634, 253, 506, 1012, 993, 971, 927, 823, 615, 199, 398, 796, 561, 107, 214, 428, 856, 697, 379, 758, 485, 970, 925, 819, 623, 215, 430, 860, 689, 363, 726, 421, 842, 669, 307, 614, 197, 394, 788, 545, 75, 150, 300, 600, 185, 370, 740, 449, 898, 781, 531, 47, 94, 188, 376, 752, 489, 978, 941, 851, 687, 343, 686, 341, 682, 349, 698, 381, 762, 509, 1018, 1021, 1011, 1007, 983, 935, 839, 647, 263, 526, 21, 42, 84, 168, 336, 672, 329, 658, 301, 602, 189, 378, 756, 481, 962, 909, 787, 559, 87, 174, 348, 696, 377, 754, 493, 986, 957, 883, 751, 471, 942, 853, 675, 335, 670, 309, 618, 221, 442, 884, 737, 459, 918, 805, 579, 143, 286, 572, 113, 226, 452, 904, 793, 571, 127, 254, 508, 1016, 1017, 1019, 1023, 1015, 999, 967, 903, 775, 519, 7, 14, 28, 56, 112, 224, 448, 896, 777, 539, 63, 126, 252, 504, 1008, 1001, 987, 959, 887, 743, 455, 910, 789, 547, 79, 158, 316, 632, 249, 498, 996, 961, 907, 799, 567, 103, 206, 412, 824, 633, 251, 502, 1004, 977, 939, 863, 695, 359, 718, 405, 810, 605, 179, 358, 716, 401, 802, 589, 147, 294, 588, 145, 290, 580, 129, 258, 516, 1}; +typedef Field Field10; + +// 11 bit field +typedef RecLinTrans StatTable11; +constexpr StatTable11 QRT_TABLE_11({1844, 72, 74, 478, 78, 862, 470, 512, 94, 0, 894}); +constexpr uint16_t LOG_TABLE_11[] = {2047, 0, 1, 1029, 2, 11, 1030, 1496, 3, 478, 12, 1912, 1031, 47, 1497, 1040, 4, 22, 479, 243, 13, 945, 1913, 1076, 1032, 678, 48, 1507, 1498, 894, 1041, 742, 5, 1771, 23, 1543, 480, 961, 244, 1923, 14, 1882, 946, 1707, 1914, 489, 1077, 1800, 1033, 1361, 679, 1051, 49, 1272, 1508, 580, 1499, 58, 895, 639, 1042, 1389, 743, 1974, 6, 956, 1772, 520, 24, 1777, 1544, 371, 481, 1567, 962, 1087, 245, 1668, 1924, 127, 15, 94, 1883, 343, 947, 33, 1708, 177, 1915, 1609, 490, 1289, 1078, 191, 1801, 254, 1034, 121, 1362, 753, 680, 525, 1052, 319, 50, 905, 1273, 394, 1509, 1442, 581, 1990, 1500, 782, 59, 451, 896, 1722, 640, 1518, 1043, 1739, 1390, 864, 744, 689, 1975, 1959, 7, 941, 957, 1268, 1773, 29, 521, 1718, 25, 1476, 1778, 721, 1545, 1893, 372, 1368, 482, 101, 1568, 1811, 963, 1480, 1088, 810, 246, 500, 1669, 789, 1925, 1863, 128, 704, 16, 88, 95, 1150, 1884, 1782, 344, 979, 948, 1348, 34, 665, 1709, 108, 178, 1554, 1916, 972, 1610, 838, 491, 725, 1290, 424, 1079, 1163, 192, 1934, 1802, 1423, 255, 1652, 1035, 1795, 122, 1985, 1363, 1549, 754, 290, 681, 1400, 526, 1183, 1053, 1249, 320, 759, 51, 1156, 906, 1832, 1274, 1897, 395, 650, 1510, 607, 1443, 549, 582, 69, 1991, 1331, 1501, 1283, 783, 543, 60, 376, 452, 1220, 897, 992, 1723, 591, 641, 271, 1519, 295, 1044, 831, 1740, 1123, 1391, 1372, 865, 217, 745, 1206, 690, 410, 1976, 357, 1960, 1062, 8, 44, 942, 891, 958, 486, 1269, 1386, 1774, 1665, 30, 188, 522, 1439, 1719, 686, 26, 1890, 1477, 1860, 1779, 105, 722, 1420, 1546, 1246, 1894, 66, 373, 268, 1369, 354, 483, 1436, 102, 265, 1569, 1572, 1812, 1617, 964, 202, 1481, 162, 1089, 1575, 811, 1405, 247, 1324, 501, 1747, 1670, 1815, 790, 1300, 1926, 913, 1864, 2021, 129, 1620, 705, 1691, 17, 1356, 89, 777, 96, 967, 1151, 826, 1885, 1319, 1783, 1171, 345, 205, 980, 531, 949, 1788, 1349, 627, 35, 1484, 666, 231, 1710, 1947, 109, 382, 179, 165, 1555, 508, 1917, 313, 973, 1214, 1611, 1092, 839, 1098, 492, 1000, 726, 1636, 1291, 1578, 425, 1188, 1080, 1176, 1164, 138, 193, 814, 1935, 615, 1803, 1679, 1424, 150, 256, 1408, 1653, 879, 1036, 738, 1796, 1970, 123, 250, 1986, 1955, 1364, 700, 1550, 1648, 755, 1327, 291, 1058, 682, 350, 1401, 1687, 527, 504, 1184, 875, 1054, 1008, 1250, 458, 321, 1750, 760, 1012, 52, 1733, 1157, 1200, 907, 1673, 1833, 845, 1275, 437, 1898, 1529, 396, 1818, 651, 1254, 1511, 210, 608, 1130, 1444, 793, 550, 1590, 583, 1839, 70, 921, 1992, 1303, 1332, 462, 1502, 634, 1284, 859, 784, 1929, 544, 405, 61, 2016, 377, 145, 453, 916, 1221, 325, 898, 985, 993, 2001, 1724, 1867, 592, 1461, 642, 1453, 272, 1226, 1520, 2024, 296, 1754, 1045, 445, 832, 1117, 1741, 132, 1124, 1104, 1392, 2008, 1373, 1847, 866, 1623, 218, 764, 746, 536, 1207, 1110, 691, 708, 411, 1137, 1977, 851, 358, 330, 1961, 1694, 1063, 1016, 9, 2045, 45, 476, 943, 20, 892, 676, 959, 1769, 487, 1880, 1270, 1359, 1387, 56, 1775, 954, 1666, 1565, 31, 92, 189, 1607, 523, 119, 1440, 903, 1720, 780, 687, 1737, 27, 939, 1891, 1474, 1478, 99, 1861, 498, 1780, 86, 106, 1346, 723, 970, 1421, 1161, 1547, 1793, 1247, 1398, 1895, 1154, 67, 605, 374, 1281, 269, 990, 1370, 829, 355, 1204, 484, 42, 1437, 1663, 103, 1888, 266, 1244, 1570, 1434, 1573, 200, 1813, 1322, 1618, 911, 965, 1354, 203, 1317, 1482, 1786, 163, 1945, 1090, 311, 1576, 998, 812, 1174, 1406, 1677, 248, 736, 1325, 698, 502, 348, 1748, 1006, 1671, 1731, 1816, 435, 791, 208, 1301, 1837, 1927, 632, 914, 2014, 1865, 983, 2022, 1451, 130, 443, 1621, 2006, 706, 534, 1692, 849, 18, 2043, 1357, 1767, 90, 952, 778, 117, 97, 937, 968, 84, 1152, 1791, 827, 1279, 1886, 40, 1320, 1432, 1784, 1352, 1172, 309, 346, 734, 206, 1729, 981, 630, 532, 441, 950, 2041, 1789, 935, 1350, 38, 628, 732, 36, 2039, 1485, 2037, 667, 1487, 232, 1902, 1711, 1489, 1948, 1379, 110, 669, 383, 570, 180, 1904, 166, 1872, 1556, 234, 509, 1533, 1918, 1491, 314, 366, 974, 1713, 1215, 285, 1612, 1381, 1093, 821, 840, 1950, 1099, 400, 493, 671, 1001, 1239, 727, 112, 1637, 280, 1292, 572, 1579, 597, 426, 385, 1189, 1822, 1081, 1906, 1177, 715, 1165, 182, 139, 1642, 194, 1874, 815, 78, 1936, 168, 616, 655, 1804, 236, 1680, 1853, 1425, 1558, 151, 800, 257, 1535, 1409, 1466, 1654, 511, 880, 1258, 1037, 1493, 739, 1073, 1797, 1920, 1971, 577, 124, 368, 251, 174, 1987, 316, 1956, 1515, 1365, 1715, 701, 807, 1551, 976, 1649, 421, 756, 287, 1328, 647, 292, 1217, 1059, 214, 683, 1383, 351, 1417, 1402, 1614, 1688, 1297, 528, 823, 505, 228, 1185, 1095, 876, 612, 1055, 1952, 1009, 872, 1251, 842, 459, 1587, 322, 402, 1751, 1458, 761, 1101, 1013, 1134, 53, 673, 1734, 1604, 1158, 495, 1201, 602, 908, 1241, 1674, 1942, 1834, 1003, 846, 1448, 1276, 114, 438, 306, 1899, 729, 1530, 567, 397, 282, 1819, 277, 652, 1639, 1255, 797, 1512, 574, 211, 418, 609, 1294, 1131, 1584, 1445, 599, 794, 564, 551, 1581, 1591, 554, 584, 387, 1840, 1629, 71, 428, 922, 557, 1993, 1824, 1304, 1231, 1333, 1191, 463, 1594, 1503, 1908, 635, 1703, 1285, 1083, 860, 390, 785, 717, 1930, 661, 545, 1179, 406, 587, 62, 184, 2017, 158, 378, 1167, 146, 1632, 454, 1644, 917, 1525, 1222, 141, 326, 1843, 899, 1876, 986, 1342, 994, 196, 2002, 431, 1725, 80, 1868, 2033, 593, 817, 1462, 74, 643, 170, 1454, 224, 273, 1938, 1227, 560, 1521, 657, 2025, 2029, 297, 618, 1755, 925, 1046, 238, 446, 338, 833, 1806, 1118, 1827, 1742, 1855, 133, 622, 1125, 1682, 1105, 1996, 1393, 1560, 2009, 1312, 1374, 1427, 1848, 1234, 867, 802, 1624, 301, 219, 153, 765, 1307, 747, 1537, 537, 1144, 1208, 259, 1111, 1194, 692, 1468, 709, 929, 412, 1411, 1138, 1336, 1978, 513, 852, 770, 359, 1656, 331, 1597, 1962, 1260, 1695, 1759, 1064, 882, 1017, 466, 10, 1495, 2046, 1028, 46, 1039, 477, 1911, 944, 1075, 21, 242, 893, 741, 677, 1506, 960, 1922, 1770, 1542, 488, 1799, 1881, 1706, 1271, 579, 1360, 1050, 1388, 1973, 57, 638, 1776, 370, 955, 519, 1667, 126, 1566, 1086, 32, 176, 93, 342, 190, 253, 1608, 1288, 524, 318, 120, 752, 1441, 1989, 904, 393, 1721, 1517, 781, 450, 688, 1958, 1738, 863, 28, 1717, 940, 1267, 1892, 1367, 1475, 720, 1479, 809, 100, 1810, 1862, 703, 499, 788, 1781, 978, 87, 1149, 107, 1553, 1347, 664, 724, 423, 971, 837, 1422, 1651, 1162, 1933, 1548, 289, 1794, 1984, 1248, 758, 1399, 1182, 1896, 649, 1155, 1831, 68, 1330, 606, 548, 375, 1219, 1282, 542, 270, 294, 991, 590, 1371, 216, 830, 1122, 356, 1061, 1205, 409, 485, 1385, 43, 890, 1438, 685, 1664, 187, 104, 1419, 1889, 1859, 267, 353, 1245, 65, 1571, 1616, 1435, 264, 1574, 1404, 201, 161, 1814, 1299, 1323, 1746, 1619, 1690, 912, 2020, 966, 825, 1355, 776, 204, 530, 1318, 1170, 1483, 230, 1787, 626, 164, 507, 1946, 381, 1091, 1097, 312, 1213, 1577, 1187, 999, 1635, 813, 614, 1175, 137, 1407, 878, 1678, 149, 249, 1954, 737, 1969, 1326, 1057, 699, 1647, 503, 874, 349, 1686, 1749, 1011, 1007, 457, 1672, 844, 1732, 1199, 1817, 1253, 436, 1528, 792, 1589, 209, 1129, 1302, 461, 1838, 920, 1928, 404, 633, 858, 915, 324, 2015, 144, 1866, 1460, 984, 2000, 2023, 1753, 1452, 1225, 131, 1103, 444, 1116, 1622, 763, 2007, 1846, 707, 1136, 535, 1109, 1693, 1015, 850, 329, 19, 675, 2044, 475, 1358, 55, 1768, 1879, 91, 1606, 953, 1564, 779, 1736, 118, 902, 98, 497, 938, 1473, 969, 1160, 85, 1345, 1153, 604, 1792, 1397, 828, 1203, 1280, 989, 1887, 1243, 41, 1662, 1321, 910, 1433, 199, 1785, 1944, 1353, 1316, 1173, 1676, 310, 997, 347, 1005, 735, 697, 207, 1836, 1730, 434, 982, 1450, 631, 2013, 533, 848, 442, 2005, 951, 116, 2042, 1766, 1790, 1278, 936, 83, 1351, 308, 39, 1431, 629, 440, 733, 1728, 37, 731, 2040, 934, 1486, 1901, 2038, 2036, 668, 569, 1488, 1378, 233, 1532, 1903, 1871, 1712, 284, 1490, 365, 1949, 399, 1380, 820, 111, 279, 670, 1238, 384, 1821, 571, 596, 181, 1641, 1905, 714, 167, 654, 1873, 77, 1557, 799, 235, 1852, 510, 1257, 1534, 1465, 1919, 576, 1492, 1072, 315, 1514, 367, 173, 975, 420, 1714, 806, 1216, 213, 286, 646, 1613, 1296, 1382, 1416, 1094, 611, 822, 227, 841, 1586, 1951, 871, 1100, 1133, 401, 1457, 494, 601, 672, 1603, 1002, 1447, 1240, 1941, 728, 566, 113, 305, 1638, 796, 281, 276, 1293, 1583, 573, 417, 1580, 553, 598, 563, 427, 556, 386, 1628, 1190, 1593, 1823, 1230, 1082, 389, 1907, 1702, 1178, 586, 716, 660, 1166, 1631, 183, 157, 140, 1842, 1643, 1524, 195, 430, 1875, 1341, 816, 73, 79, 2032, 1937, 559, 169, 223, 617, 924, 656, 2028, 1805, 1826, 237, 337, 1681, 1995, 1854, 621, 1426, 1233, 1559, 1311, 152, 1306, 801, 300, 258, 1193, 1536, 1143, 1410, 1335, 1467, 928, 1655, 1596, 512, 769, 881, 465, 1259, 1758, 1038, 1910, 1494, 1027, 740, 1505, 1074, 241, 1798, 1705, 1921, 1541, 1972, 637, 578, 1049, 125, 1085, 369, 518, 252, 1287, 175, 341, 1988, 392, 317, 751, 1957, 862, 1516, 449, 1366, 719, 1716, 1266, 702, 787, 808, 1809, 1552, 663, 977, 1148, 1650, 1932, 422, 836, 757, 1181, 288, 1983, 1329, 547, 648, 1830, 293, 589, 1218, 541, 1060, 408, 215, 1121, 684, 186, 1384, 889, 352, 64, 1418, 1858, 1403, 160, 1615, 263, 1689, 2019, 1298, 1745, 529, 1169, 824, 775, 506, 380, 229, 625, 1186, 1634, 1096, 1212, 877, 148, 613, 136, 1056, 1646, 1953, 1968, 1010, 456, 873, 1685, 1252, 1527, 843, 1198, 460, 919, 1588, 1128, 323, 143, 403, 857, 1752, 1224, 1459, 1999, 762, 1845, 1102, 1115, 1014, 328, 1135, 1108, 54, 1878, 674, 474, 1735, 901, 1605, 1563, 1159, 1344, 496, 1472, 1202, 988, 603, 1396, 909, 198, 1242, 1661, 1675, 996, 1943, 1315, 1835, 433, 1004, 696, 847, 2004, 1449, 2012, 1277, 82, 115, 1765, 439, 1727, 307, 1430, 1900, 2035, 730, 933, 1531, 1870, 568, 1377, 398, 819, 283, 364, 1820, 595, 278, 1237, 653, 76, 1640, 713, 1256, 1464, 798, 1851, 1513, 172, 575, 1071, 212, 645, 419, 805, 610, 226, 1295, 1415, 1132, 1456, 1585, 870, 1446, 1940, 600, 1602, 795, 275, 565, 304, 552, 562, 1582, 416, 1592, 1229, 555, 1627, 585, 659, 388, 1701, 1841, 1523, 1630, 156, 72, 2031, 429, 1340, 923, 2027, 558, 222, 1994, 620, 1825, 336, 1305, 299, 1232, 1310, 1334, 927, 1192, 1142, 464, 1757, 1595, 768, 1504, 240, 1909, 1026, 636, 1048, 1704, 1540, 1286, 340, 1084, 517, 861, 448, 391, 750, 786, 1808, 718, 1265, 1931, 835, 662, 1147, 546, 1829, 1180, 1982, 407, 1120, 588, 540, 63, 1857, 185, 888, 2018, 1744, 159, 262, 379, 624, 1168, 774, 147, 135, 1633, 1211, 455, 1684, 1645, 1967, 918, 1127, 1526, 1197, 1223, 1998, 142, 856, 327, 1107, 1844, 1114, 900, 1562, 1877, 473, 987, 1395, 1343, 1471, 995, 1314, 197, 1660, 2003, 2011, 432, 695, 1726, 1429, 81, 1764, 1869, 1376, 2034, 932, 594, 1236, 818, 363, 1463, 1850, 75, 712, 644, 804, 171, 1070, 1455, 869, 225, 1414, 274, 303, 1939, 1601, 1228, 1626, 561, 415, 1522, 155, 658, 1700, 2026, 221, 2030, 1339, 298, 1309, 619, 335, 1756, 767, 926, 1141, 1047, 1539, 239, 1025, 447, 749, 339, 516, 834, 1146, 1807, 1264, 1119, 539, 1828, 1981, 1743, 261, 1856, 887, 134, 1210, 623, 773, 1126, 1196, 1683, 1966, 1106, 1113, 1997, 855, 1394, 1470, 1561, 472, 2010, 694, 1313, 1659, 1375, 931, 1428, 1763, 1849, 711, 1235, 362, 868, 1413, 803, 1069, 1625, 414, 302, 1600, 220, 1338, 154, 1699, 766, 1140, 1308, 334, 748, 515, 1538, 1024, 538, 1980, 1145, 1263, 1209, 772, 260, 886, 1112, 854, 1195, 1965, 693, 1658, 1469, 471, 710, 361, 930, 1762, 413, 1599, 1412, 1068, 1139, 333, 1337, 1698, 1979, 1262, 514, 1023, 853, 1964, 771, 885, 360, 1761, 1657, 470, 332, 1697, 1598, 1067, 1963, 884, 1261, 1022, 1696, 1066, 1760, 469, 1065, 468, 883, 1021, 1018, 1019, 467, 1020}; +constexpr uint16_t EXP_TABLE_11[] = {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 5, 10, 20, 40, 80, 160, 320, 640, 1280, 517, 1034, 17, 34, 68, 136, 272, 544, 1088, 133, 266, 532, 1064, 85, 170, 340, 680, 1360, 677, 1354, 657, 1314, 577, 1154, 257, 514, 1028, 13, 26, 52, 104, 208, 416, 832, 1664, 1285, 527, 1054, 57, 114, 228, 456, 912, 1824, 1605, 1167, 283, 566, 1132, 221, 442, 884, 1768, 1493, 943, 1886, 1721, 1399, 747, 1494, 937, 1874, 1697, 1351, 651, 1302, 553, 1106, 161, 322, 644, 1288, 533, 1066, 81, 162, 324, 648, 1296, 549, 1098, 145, 290, 580, 1160, 277, 554, 1108, 173, 346, 692, 1384, 725, 1450, 849, 1698, 1345, 647, 1294, 537, 1074, 97, 194, 388, 776, 1552, 1061, 79, 158, 316, 632, 1264, 485, 970, 1940, 1837, 1631, 1211, 371, 742, 1484, 925, 1850, 1649, 1255, 459, 918, 1836, 1629, 1215, 379, 758, 1516, 989, 1978, 1905, 1767, 1483, 915, 1830, 1609, 1175, 299, 598, 1196, 349, 698, 1396, 749, 1498, 945, 1890, 1729, 1415, 779, 1558, 1065, 87, 174, 348, 696, 1392, 741, 1482, 913, 1826, 1601, 1159, 267, 534, 1068, 93, 186, 372, 744, 1488, 933, 1866, 1681, 1319, 587, 1174, 297, 594, 1188, 333, 666, 1332, 621, 1242, 433, 866, 1732, 1421, 799, 1598, 1145, 247, 494, 988, 1976, 1909, 1775, 1499, 947, 1894, 1737, 1431, 811, 1622, 1193, 343, 686, 1372, 701, 1402, 753, 1506, 961, 1922, 1793, 1543, 1035, 19, 38, 76, 152, 304, 608, 1216, 389, 778, 1556, 1069, 95, 190, 380, 760, 1520, 997, 1994, 1937, 1831, 1611, 1171, 291, 582, 1164, 285, 570, 1140, 237, 474, 948, 1896, 1749, 1455, 859, 1718, 1385, 727, 1454, 857, 1714, 1377, 711, 1422, 793, 1586, 1121, 199, 398, 796, 1592, 1141, 239, 478, 956, 1912, 1781, 1519, 987, 1974, 1897, 1751, 1451, 851, 1702, 1353, 663, 1326, 601, 1202, 353, 706, 1412, 781, 1562, 1073, 103, 206, 412, 824, 1648, 1253, 463, 926, 1852, 1661, 1279, 507, 1014, 2028, 2013, 1983, 1915, 1779, 1507, 963, 1926, 1801, 1559, 1067, 83, 166, 332, 664, 1328, 613, 1226, 401, 802, 1604, 1165, 287, 574, 1148, 253, 506, 1012, 2024, 2005, 1967, 1883, 1715, 1379, 707, 1414, 777, 1554, 1057, 71, 142, 284, 568, 1136, 229, 458, 916, 1832, 1621, 1199, 347, 694, 1388, 733, 1466, 881, 1762, 1473, 903, 1806, 1561, 1079, 107, 214, 428, 856, 1712, 1381, 719, 1438, 825, 1650, 1249, 455, 910, 1820, 1597, 1151, 251, 502, 1004, 2008, 1973, 1903, 1755, 1459, 867, 1734, 1417, 791, 1582, 1113, 183, 366, 732, 1464, 885, 1770, 1489, 935, 1870, 1689, 1335, 619, 1238, 425, 850, 1700, 1357, 671, 1342, 633, 1266, 481, 962, 1924, 1805, 1567, 1083, 115, 230, 460, 920, 1840, 1637, 1231, 411, 822, 1644, 1245, 447, 894, 1788, 1533, 1023, 2046, 2041, 2039, 2027, 2003, 1955, 1859, 1667, 1283, 515, 1030, 9, 18, 36, 72, 144, 288, 576, 1152, 261, 522, 1044, 45, 90, 180, 360, 720, 1440, 837, 1674, 1297, 551, 1102, 153, 306, 612, 1224, 405, 810, 1620, 1197, 351, 702, 1404, 765, 1530, 1009, 2018, 1985, 1927, 1803, 1555, 1059, 67, 134, 268, 536, 1072, 101, 202, 404, 808, 1616, 1189, 335, 670, 1340, 637, 1274, 497, 994, 1988, 1933, 1823, 1595, 1139, 227, 454, 908, 1816, 1589, 1135, 219, 438, 876, 1752, 1461, 879, 1758, 1465, 887, 1774, 1497, 951, 1902, 1753, 1463, 875, 1750, 1449, 855, 1710, 1369, 695, 1390, 729, 1458, 865, 1730, 1409, 775, 1550, 1049, 55, 110, 220, 440, 880, 1760, 1477, 911, 1822, 1593, 1143, 235, 470, 940, 1880, 1717, 1391, 731, 1462, 873, 1746, 1441, 839, 1678, 1305, 567, 1134, 217, 434, 868, 1736, 1429, 815, 1630, 1209, 375, 750, 1500, 957, 1914, 1777, 1511, 971, 1942, 1833, 1623, 1195, 339, 678, 1356, 669, 1338, 625, 1250, 449, 898, 1796, 1549, 1055, 59, 118, 236, 472, 944, 1888, 1733, 1423, 795, 1590, 1129, 215, 430, 860, 1720, 1397, 751, 1502, 953, 1906, 1761, 1479, 907, 1814, 1577, 1111, 171, 342, 684, 1368, 693, 1386, 721, 1442, 833, 1666, 1281, 519, 1038, 25, 50, 100, 200, 400, 800, 1600, 1157, 271, 542, 1084, 125, 250, 500, 1000, 2000, 1957, 1871, 1691, 1331, 611, 1222, 393, 786, 1572, 1101, 159, 318, 636, 1272, 501, 1002, 2004, 1965, 1887, 1723, 1395, 739, 1478, 905, 1810, 1569, 1095, 139, 278, 556, 1112, 181, 362, 724, 1448, 853, 1706, 1361, 679, 1358, 665, 1330, 609, 1218, 385, 770, 1540, 1037, 31, 62, 124, 248, 496, 992, 1984, 1925, 1807, 1563, 1075, 99, 198, 396, 792, 1584, 1125, 207, 414, 828, 1656, 1269, 495, 990, 1980, 1917, 1791, 1531, 1011, 2022, 1993, 1943, 1835, 1619, 1187, 323, 646, 1292, 541, 1082, 113, 226, 452, 904, 1808, 1573, 1103, 155, 310, 620, 1240, 437, 874, 1748, 1453, 863, 1726, 1401, 759, 1518, 985, 1970, 1889, 1735, 1419, 787, 1574, 1097, 151, 302, 604, 1208, 373, 746, 1492, 941, 1882, 1713, 1383, 715, 1430, 809, 1618, 1185, 327, 654, 1308, 573, 1146, 241, 482, 964, 1928, 1813, 1583, 1115, 179, 358, 716, 1432, 821, 1642, 1233, 423, 846, 1692, 1341, 639, 1278, 505, 1010, 2020, 1997, 1951, 1851, 1651, 1251, 451, 902, 1804, 1565, 1087, 123, 246, 492, 984, 1968, 1893, 1743, 1435, 819, 1638, 1225, 407, 814, 1628, 1213, 383, 766, 1532, 1021, 2042, 2033, 2023, 1995, 1939, 1827, 1603, 1155, 259, 518, 1036, 29, 58, 116, 232, 464, 928, 1856, 1669, 1295, 539, 1078, 105, 210, 420, 840, 1680, 1317, 591, 1182, 313, 626, 1252, 461, 922, 1844, 1645, 1247, 443, 886, 1772, 1501, 959, 1918, 1785, 1527, 1003, 2006, 1961, 1879, 1707, 1363, 675, 1350, 649, 1298, 545, 1090, 129, 258, 516, 1032, 21, 42, 84, 168, 336, 672, 1344, 645, 1290, 529, 1058, 65, 130, 260, 520, 1040, 37, 74, 148, 296, 592, 1184, 325, 650, 1300, 557, 1114, 177, 354, 708, 1416, 789, 1578, 1105, 167, 334, 668, 1336, 629, 1258, 465, 930, 1860, 1677, 1311, 571, 1142, 233, 466, 932, 1864, 1685, 1327, 603, 1206, 361, 722, 1444, 845, 1690, 1329, 615, 1230, 409, 818, 1636, 1229, 415, 830, 1660, 1277, 511, 1022, 2044, 2045, 2047, 2043, 2035, 2019, 1987, 1923, 1795, 1539, 1027, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 1029, 15, 30, 60, 120, 240, 480, 960, 1920, 1797, 1551, 1051, 51, 102, 204, 408, 816, 1632, 1221, 399, 798, 1596, 1149, 255, 510, 1020, 2040, 2037, 2031, 2011, 1971, 1891, 1731, 1411, 771, 1542, 1033, 23, 46, 92, 184, 368, 736, 1472, 901, 1802, 1553, 1063, 75, 150, 300, 600, 1200, 357, 714, 1428, 813, 1626, 1201, 359, 718, 1436, 829, 1658, 1265, 487, 974, 1948, 1853, 1663, 1275, 499, 998, 1996, 1949, 1855, 1659, 1267, 483, 966, 1932, 1821, 1599, 1147, 243, 486, 972, 1944, 1845, 1647, 1243, 435, 870, 1740, 1437, 831, 1662, 1273, 503, 1006, 2012, 1981, 1919, 1787, 1523, 995, 1990, 1929, 1815, 1579, 1107, 163, 326, 652, 1304, 565, 1130, 209, 418, 836, 1672, 1301, 559, 1118, 185, 370, 740, 1480, 917, 1834, 1617, 1191, 331, 662, 1324, 605, 1210, 369, 738, 1476, 909, 1818, 1585, 1127, 203, 406, 812, 1624, 1205, 367, 734, 1468, 893, 1786, 1521, 999, 1998, 1945, 1847, 1643, 1235, 419, 838, 1676, 1309, 575, 1150, 249, 498, 996, 1992, 1941, 1839, 1627, 1203, 355, 710, 1420, 797, 1594, 1137, 231, 462, 924, 1848, 1653, 1263, 475, 950, 1900, 1757, 1471, 891, 1782, 1513, 983, 1966, 1881, 1719, 1387, 723, 1446, 841, 1682, 1313, 583, 1166, 281, 562, 1124, 205, 410, 820, 1640, 1237, 431, 862, 1724, 1405, 767, 1534, 1017, 2034, 2017, 1991, 1931, 1811, 1571, 1091, 131, 262, 524, 1048, 53, 106, 212, 424, 848, 1696, 1349, 655, 1310, 569, 1138, 225, 450, 900, 1800, 1557, 1071, 91, 182, 364, 728, 1456, 869, 1738, 1425, 807, 1614, 1177, 311, 622, 1244, 445, 890, 1780, 1517, 991, 1982, 1913, 1783, 1515, 979, 1958, 1865, 1687, 1323, 595, 1190, 329, 658, 1316, 589, 1178, 305, 610, 1220, 397, 794, 1588, 1133, 223, 446, 892, 1784, 1525, 1007, 2014, 1977, 1911, 1771, 1491, 931, 1862, 1673, 1303, 555, 1110, 169, 338, 676, 1352, 661, 1322, 593, 1186, 321, 642, 1284, 525, 1050, 49, 98, 196, 392, 784, 1568, 1093, 143, 286, 572, 1144, 245, 490, 980, 1960, 1877, 1711, 1371, 691, 1382, 713, 1426, 801, 1602, 1153, 263, 526, 1052, 61, 122, 244, 488, 976, 1952, 1861, 1679, 1307, 563, 1126, 201, 402, 804, 1608, 1173, 303, 606, 1212, 381, 762, 1524, 1005, 2010, 1969, 1895, 1739, 1427, 803, 1606, 1161, 279, 558, 1116, 189, 378, 756, 1512, 981, 1962, 1873, 1703, 1355, 659, 1318, 585, 1170, 289, 578, 1156, 269, 538, 1076, 109, 218, 436, 872, 1744, 1445, 847, 1694, 1337, 631, 1262, 473, 946, 1892, 1741, 1439, 827, 1654, 1257, 471, 942, 1884, 1725, 1407, 763, 1526, 1001, 2002, 1953, 1863, 1675, 1299, 547, 1094, 137, 274, 548, 1096, 149, 298, 596, 1192, 341, 682, 1364, 685, 1370, 689, 1378, 705, 1410, 769, 1538, 1025, 7, 14, 28, 56, 112, 224, 448, 896, 1792, 1541, 1039, 27, 54, 108, 216, 432, 864, 1728, 1413, 783, 1566, 1081, 119, 238, 476, 952, 1904, 1765, 1487, 923, 1846, 1641, 1239, 427, 854, 1708, 1373, 703, 1406, 761, 1522, 993, 1986, 1921, 1799, 1547, 1043, 35, 70, 140, 280, 560, 1120, 197, 394, 788, 1576, 1109, 175, 350, 700, 1400, 757, 1514, 977, 1954, 1857, 1671, 1291, 531, 1062, 73, 146, 292, 584, 1168, 293, 586, 1172, 301, 602, 1204, 365, 730, 1460, 877, 1754, 1457, 871, 1742, 1433, 823, 1646, 1241, 439, 878, 1756, 1469, 895, 1790, 1529, 1015, 2030, 2009, 1975, 1899, 1747, 1443, 835, 1670, 1289, 535, 1070, 89, 178, 356, 712, 1424, 805, 1610, 1169, 295, 590, 1180, 317, 634, 1268, 493, 986, 1972, 1901, 1759, 1467, 883, 1766, 1481, 919, 1838, 1625, 1207, 363, 726, 1452, 861, 1722, 1393, 743, 1486, 921, 1842, 1633, 1223, 395, 790, 1580, 1117, 191, 382, 764, 1528, 1013, 2026, 2001, 1959, 1867, 1683, 1315, 579, 1158, 265, 530, 1060, 77, 154, 308, 616, 1232, 421, 842, 1684, 1325, 607, 1214, 377, 754, 1508, 973, 1946, 1841, 1639, 1227, 403, 806, 1612, 1181, 319, 638, 1276, 509, 1018, 2036, 2029, 2015, 1979, 1907, 1763, 1475, 899, 1798, 1545, 1047, 43, 86, 172, 344, 688, 1376, 709, 1418, 785, 1570, 1089, 135, 270, 540, 1080, 117, 234, 468, 936, 1872, 1701, 1359, 667, 1334, 617, 1234, 417, 834, 1668, 1293, 543, 1086, 121, 242, 484, 968, 1936, 1829, 1615, 1179, 307, 614, 1228, 413, 826, 1652, 1261, 479, 958, 1916, 1789, 1535, 1019, 2038, 2025, 2007, 1963, 1875, 1699, 1347, 643, 1286, 521, 1042, 33, 66, 132, 264, 528, 1056, 69, 138, 276, 552, 1104, 165, 330, 660, 1320, 597, 1194, 337, 674, 1348, 653, 1306, 561, 1122, 193, 386, 772, 1544, 1045, 47, 94, 188, 376, 752, 1504, 965, 1930, 1809, 1575, 1099, 147, 294, 588, 1176, 309, 618, 1236, 429, 858, 1716, 1389, 735, 1470, 889, 1778, 1505, 967, 1934, 1817, 1591, 1131, 211, 422, 844, 1688, 1333, 623, 1246, 441, 882, 1764, 1485, 927, 1854, 1657, 1271, 491, 982, 1964, 1885, 1727, 1403, 755, 1510, 969, 1938, 1825, 1607, 1163, 275, 550, 1100, 157, 314, 628, 1256, 469, 938, 1876, 1709, 1375, 699, 1398, 745, 1490, 929, 1858, 1665, 1287, 523, 1046, 41, 82, 164, 328, 656, 1312, 581, 1162, 273, 546, 1092, 141, 282, 564, 1128, 213, 426, 852, 1704, 1365, 687, 1374, 697, 1394, 737, 1474, 897, 1794, 1537, 1031, 11, 22, 44, 88, 176, 352, 704, 1408, 773, 1546, 1041, 39, 78, 156, 312, 624, 1248, 453, 906, 1812, 1581, 1119, 187, 374, 748, 1496, 949, 1898, 1745, 1447, 843, 1686, 1321, 599, 1198, 345, 690, 1380, 717, 1434, 817, 1634, 1217, 391, 782, 1564, 1085, 127, 254, 508, 1016, 2032, 2021, 1999, 1947, 1843, 1635, 1219, 387, 774, 1548, 1053, 63, 126, 252, 504, 1008, 2016, 1989, 1935, 1819, 1587, 1123, 195, 390, 780, 1560, 1077, 111, 222, 444, 888, 1776, 1509, 975, 1950, 1849, 1655, 1259, 467, 934, 1868, 1693, 1343, 635, 1270, 489, 978, 1956, 1869, 1695, 1339, 627, 1254, 457, 914, 1828, 1613, 1183, 315, 630, 1260, 477, 954, 1908, 1773, 1503, 955, 1910, 1769, 1495, 939, 1878, 1705, 1367, 683, 1366, 681, 1362, 673, 1346, 641, 1282, 513, 1026, 1}; +typedef Field Field11; + +// 12 bit field +typedef RecLinTrans StatTable12; +constexpr StatTable12 QRT_TABLE_12({72, 3088, 3090, 520, 3094, 3458, 512, 272, 3078, 0, 3490, 1444}); +constexpr uint16_t LOG_TABLE_12[] = {4095, 0, 1729, 1, 3458, 2, 1730, 272, 1092, 273, 1731, 1297, 3459, 2743, 2001, 3, 2821, 4, 2002, 2034, 3460, 544, 3026, 2744, 1093, 2829, 377, 274, 3730, 1298, 1732, 1689, 455, 1690, 1733, 3015, 3731, 3987, 3763, 1299, 1094, 401, 2273, 2830, 660, 275, 378, 254, 2822, 1569, 463, 5, 2106, 2035, 2003, 2793, 1364, 2745, 3027, 3241, 3461, 1864, 3418, 545, 2184, 546, 3419, 3777, 3462, 2594, 649, 1865, 1365, 2730, 1621, 2746, 1397, 3242, 3028, 3101, 2823, 1391, 2130, 1570, 4002, 6, 464, 614, 2389, 2794, 2004, 2514, 2107, 1961, 1983, 2036, 456, 519, 3298, 1691, 2192, 3016, 1734, 3519, 3835, 1300, 3764, 816, 3732, 3747, 427, 3988, 3093, 255, 379, 3942, 661, 806, 875, 276, 1095, 2306, 3593, 402, 1052, 2831, 2274, 4040, 3913, 4041, 2275, 845, 1053, 3065, 1411, 2832, 1096, 1508, 228, 2307, 2378, 403, 3594, 2175, 3094, 16, 364, 256, 3350, 3943, 380, 1841, 3126, 277, 876, 337, 662, 2294, 735, 807, 457, 3513, 3120, 520, 3859, 1692, 3299, 2629, 1636, 3520, 1735, 475, 2193, 3331, 2343, 3017, 23, 3989, 428, 2136, 3733, 1477, 148, 3748, 3836, 3437, 3690, 1301, 3712, 817, 3765, 1855, 2185, 330, 2248, 547, 932, 3778, 3420, 682, 3921, 1866, 650, 3965, 3463, 526, 1153, 2595, 1469, 3102, 3029, 492, 1398, 1232, 2545, 3243, 1366, 2986, 1381, 2731, 2156, 2747, 1622, 673, 727, 2037, 1984, 31, 2108, 626, 1576, 1962, 2390, 3287, 2535, 2795, 2604, 2515, 2005, 3681, 2824, 2268, 4035, 1392, 1227, 1571, 2131, 3908, 2781, 615, 465, 164, 4003, 3579, 1674, 7, 1547, 8, 1675, 4019, 4004, 4068, 2574, 3580, 2782, 1551, 699, 616, 3140, 165, 466, 1889, 2825, 1088, 3237, 2269, 1957, 1393, 4036, 423, 12, 3909, 2132, 3116, 1228, 928, 3904, 1572, 728, 512, 1745, 2038, 2093, 32, 1985, 791, 984, 1963, 1577, 1679, 2109, 2938, 3570, 627, 760, 3682, 2006, 1698, 2605, 3791, 2066, 2516, 2391, 995, 4023, 3288, 2464, 2796, 2536, 1802, 2186, 1563, 1147, 331, 754, 548, 2249, 1189, 1493, 683, 3421, 1078, 933, 4008, 263, 3779, 3365, 2596, 1154, 1441, 3464, 3378, 2204, 527, 3922, 119, 965, 1867, 4072, 3966, 651, 3700, 1752, 674, 1623, 77, 2157, 554, 3865, 2748, 1367, 2762, 3206, 2987, 1877, 2732, 1382, 2578, 1470, 1614, 1071, 3103, 1324, 493, 3030, 3815, 1346, 3244, 2546, 1589, 1399, 217, 3584, 1233, 3914, 2786, 2059, 4042, 3977, 846, 2276, 3804, 2661, 2833, 1412, 1134, 1054, 313, 2411, 3066, 1555, 2176, 3595, 2233, 2379, 443, 1599, 404, 1097, 2635, 2255, 1509, 2882, 2308, 229, 2045, 3198, 808, 736, 703, 663, 886, 2221, 2295, 3127, 858, 2961, 278, 179, 338, 877, 3161, 3095, 371, 620, 17, 3110, 257, 365, 1663, 3885, 1842, 381, 768, 3351, 48, 2402, 3944, 2456, 1856, 3766, 1918, 3713, 3144, 1760, 818, 3837, 4049, 2355, 3438, 3305, 1302, 3691, 1195, 24, 3723, 921, 3990, 169, 2137, 429, 3611, 238, 3749, 149, 2866, 3734, 1930, 1315, 1478, 458, 4090, 3997, 3514, 1669, 521, 3121, 470, 2956, 2630, 3300, 2997, 3860, 3373, 1542, 1693, 415, 3018, 2344, 2420, 2194, 1175, 1893, 3332, 1637, 298, 1213, 3521, 3403, 476, 1736, 3002, 3276, 3003, 1737, 3007, 3404, 598, 1653, 477, 1638, 3549, 1702, 299, 208, 3522, 1214, 3258, 416, 2949, 3280, 3019, 2428, 2421, 2345, 2897, 774, 3333, 1894, 2010, 2195, 945, 3618, 1176, 459, 3011, 2817, 4091, 871, 3515, 3998, 2590, 3686, 471, 3122, 1504, 1670, 3677, 2152, 522, 1741, 1694, 1543, 1084, 3861, 3811, 750, 3374, 2957, 764, 2657, 2631, 1538, 2998, 3301, 1926, 2457, 1911, 2241, 1857, 3474, 1919, 3767, 602, 3822, 819, 1761, 104, 3714, 387, 2520, 3145, 2713, 1196, 3692, 1975, 3306, 954, 3408, 1303, 3838, 2853, 572, 4050, 1204, 3439, 2356, 2070, 2489, 1479, 1316, 798, 3735, 481, 3427, 1931, 239, 711, 1425, 3750, 3795, 2867, 150, 3631, 25, 142, 2724, 3724, 1657, 3991, 922, 1487, 98, 3612, 430, 2688, 170, 2609, 3531, 2138, 3915, 2288, 3292, 2787, 2876, 4043, 2060, 71, 2483, 3805, 2277, 3553, 3978, 3953, 2918, 847, 3222, 3067, 2412, 4027, 1055, 3498, 2807, 314, 2662, 689, 1642, 2834, 1992, 1135, 1413, 3559, 999, 2046, 230, 2978, 2883, 3180, 3170, 2309, 1098, 303, 1012, 2636, 3933, 1510, 2256, 2618, 1556, 2395, 1848, 2177, 2694, 2234, 3596, 3037, 1706, 405, 1600, 898, 2380, 2701, 1334, 444, 3481, 3945, 2403, 2167, 3352, 85, 1806, 49, 3886, 835, 2283, 1843, 1499, 769, 382, 3526, 3096, 1047, 396, 372, 840, 18, 621, 2540, 3606, 1664, 366, 2054, 3111, 979, 212, 258, 3199, 436, 3343, 809, 2800, 704, 737, 3891, 3053, 2296, 2222, 2435, 664, 3262, 1449, 887, 3075, 3162, 878, 3851, 180, 2468, 3318, 339, 3128, 3448, 1946, 859, 1218, 279, 2962, 1527, 1548, 2571, 420, 9, 3788, 4020, 1676, 2090, 1611, 3581, 2575, 1749, 4005, 1144, 1438, 4069, 295, 1890, 467, 2953, 3141, 2352, 2863, 166, 2783, 2408, 2042, 1552, 45, 617, 700, 176, 3284, 1573, 3905, 2778, 1229, 1378, 3962, 929, 13, 732, 2172, 3910, 3328, 3117, 2133, 3709, 2826, 3023, 269, 1089, 3984, 2270, 3238, 2103, 516, 424, 4037, 3090, 1958, 2127, 3774, 1394, 832, 1803, 2537, 3603, 2465, 1943, 2432, 2797, 2392, 1331, 2615, 996, 3950, 3289, 4024, 1989, 761, 747, 2587, 3683, 595, 1699, 2007, 2425, 1908, 2517, 2067, 2710, 2606, 2721, 795, 3792, 729, 3959, 2100, 513, 2349, 2039, 1746, 3785, 744, 792, 1986, 829, 2094, 2097, 3392, 33, 1519, 628, 3571, 3395, 2110, 2901, 2497, 2939, 985, 1242, 1777, 1964, 36, 1680, 1578, 3486, 90, 1234, 3585, 1581, 1400, 352, 3647, 218, 1347, 1117, 778, 3245, 3489, 1590, 2547, 1023, 1471, 721, 1683, 1615, 4084, 3104, 1072, 3898, 939, 3816, 3031, 3337, 1325, 39, 2924, 494, 1753, 988, 1357, 675, 2650, 78, 1624, 3083, 1898, 2749, 3866, 1816, 2158, 2447, 1245, 555, 1967, 2579, 1383, 3357, 1878, 3537, 500, 2733, 1368, 2014, 3659, 2763, 3044, 2988, 3207, 1780, 2187, 609, 1724, 1564, 1631, 332, 1148, 3574, 3398, 1190, 2250, 853, 755, 4014, 2199, 549, 590, 3780, 264, 2566, 934, 1811, 631, 4009, 1494, 1522, 1007, 684, 3271, 1079, 3422, 949, 2144, 3701, 652, 2930, 4073, 2113, 54, 3967, 3923, 1262, 2904, 120, 3622, 1868, 966, 1162, 3366, 3230, 2027, 2597, 2942, 1442, 1155, 288, 1037, 528, 2205, 2500, 3465, 1180, 636, 3379, 910, 3380, 637, 639, 3466, 1935, 641, 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1157, 3266, 3368, 1310, 1129, 3880, 507, 3232, 1184, 1319, 801, 644, 2029, 450, 3432, 223, 668, 2599, 3753, 2209, 2906, 1060, 1253, 2526, 561, 122, 3925, 2439, 2335, 3153, 2316, 1264, 2675, 1428, 2504, 242, 2078, 1164, 1715, 321, 968, 1826, 2226, 1870, 3740, 357, 3624, 3215, 714, 3385, 2146, 2682, 2870, 1041, 1771, 3703, 584, 346, 1405, 486, 654, 2300, 915, 3798, 1340, 2932, 3503, 2115, 532, 153, 4075, 1832, 2555, 1455, 63, 3639, 3057, 3969, 3634, 2330, 56, 1107, 2647, 1813, 3656, 3534, 936, 3895, 3644, 1114, 3268, 2563, 1721, 4011, 2141, 1159, 633, 3227, 592, 2707, 2612, 1940, 741, 3782, 2494, 1239, 3325, 2775, 266, 2124, 292, 173, 1435, 2568, 3471, 101, 569, 951, 95, 1484, 3424, 708, 1535, 1081, 2814, 3674, 3273, 3255, 3615, 2946, 2691, 895, 1009, 3177, 2480, 68, 2804, 686, 1496, 2164, 393, 976, 3072, 1524, 1446, 433, 2189, 813, 3590, 803, 2386, 611, 646, 2727, 3727, 2031, 1726, 2740, 452, 251, 3415, 1566, 3347, 334, 225, 3062, 1633, 2626, 145, 3434, 2601, 28, 4032, 3576, 1466, 670, 1150, 327, 3974, 1131, 2252, 440, 3882, 1660, 2218, 855, 3400, 2417, 3994, 3370, 2453, 1192, 1312, 3720, 1321, 1586, 3203, 551, 1490, 1186, 2201, 116, 3137, 4016, 3234, 925, 757, 1799, 3567, 509, 195, 2080, 3868, 1280, 1166, 3309, 1276, 1818, 1900, 2845, 957, 2506, 2966, 2751, 244, 1122, 1828, 1767, 1822, 557, 1306, 970, 1247, 2667, 1795, 2449, 323, 3411, 2160, 1531, 2120, 1717, 1755, 1170, 3193, 2228, 694, 990, 1872, 3695, 1978, 3742, 1359, 1292, 359, 3508, 1222, 677, 3313, 80, 3217, 2973, 2652, 3544, 1199, 3626, 3387, 2716, 1606, 3085, 1352, 716, 1626, 283, 124, 3841, 2839, 1782, 110, 563, 3209, 3872, 1950, 2990, 2528, 537, 3046, 2890, 2856, 1255, 4053, 2908, 3661, 2364, 1062, 133, 1284, 2765, 1370, 863, 783, 3755, 1788, 2016, 2211, 575, 1271, 3539, 1266, 2359, 1880, 199, 187, 2318, 1430, 3250, 3132, 2735, 2073, 2677, 502, 904, 1969, 1647, 3442, 3927, 2084, 2581, 2441, 1031, 158, 2337, 1385, 3452, 3155, 1207, 4062, 3359, 92, 3671, 390, 65, 3322, 1236, 3641, 2560, 1463, 3059, 3587, 248, 3971, 3717, 3564, 1583, 1712, 354, 2332, 2523, 1402, 343, 2552, 3636, 1109, 2475, 1126, 220, 3148, 58, 3649, 2323, 107, 534, 780, 130, 155, 1028, 184, 3247, 1349, 2970, 3190, 3505, 192, 1119, 2117, 1764, 1457, 3825, 3187, 1025, 1460, 2557, 2549, 2472, 2755, 1592, 1834, 3828, 3491, 1418, 822, 4077, 882, 3106, 3800, 1595, 4086, 411, 1914, 917, 2934, 2460, 1885, 3900, 2758, 1342, 1074, 961, 1473, 3855, 1837, 1407, 2264, 723, 488, 2244, 1860, 656, 1685, 1997, 2302, 3831, 2510, 1617, 348, 4080, 3079, 496, 605, 586, 2926, 2023, 1140, 41, 3705, 3770, 1327, 1904, 825, 1773, 3494, 2872, 3033, 3166, 1043, 3477, 3847, 3339, 941, 204, 1922, 2148, 2849, 3818, 2684, 1421, 3548, 1701, 3257, 207, 597, 1652, 3006, 3275, 2948, 3279, 2896, 2427, 944, 3617, 2009, 773, 763, 2656, 1925, 1537, 3810, 749, 1083, 1740, 3010, 2816, 2589, 870, 3676, 2151, 1503, 3685, 710, 1424, 3630, 3794, 480, 3426, 797, 2488, 141, 2723, 1486, 1656, 2608, 3530, 2687, 97, 2852, 571, 2069, 1203, 953, 3407, 1974, 2712, 1910, 2240, 601, 3473, 386, 2519, 103, 3821, 834, 2282, 3525, 1498, 84, 1805, 2166, 3480, 1046, 395, 2539, 839, 978, 211, 2053, 3605, 3447, 1945, 1526, 1217, 2467, 3317, 3850, 3074, 435, 3342, 3890, 2799, 3261, 1448, 2434, 3052, 302, 1011, 2617, 3932, 3179, 3169, 2977, 998, 2394, 1847, 3036, 2693, 2700, 1333, 897, 1705, 688, 1641, 3558, 1991, 3497, 2806, 4026, 3221, 2287, 3291, 70, 2875, 3952, 2917, 3552, 2482, 1116, 777, 1022, 3488, 351, 3646, 1580, 89, 720, 1682, 3897, 4083, 38, 2923, 3336, 938, 2013, 3658, 1779, 3043, 3536, 499, 3356, 1966, 987, 1356, 3082, 2649, 2446, 1244, 1815, 1897, 1261, 2903, 1161, 3621, 2112, 53, 2929, 2143, 3229, 2026, 287, 2941, 1179, 635, 2499, 1036, 1521, 1006, 948, 3270, 1810, 630, 2565, 589, 608, 1723, 3573, 1630, 4013, 2198, 852, 3397, 1330, 2614, 1988, 3949, 1942, 2431, 3602, 831, 746, 2586, 2424, 594, 2720, 794, 2709, 1907, 1241, 1776, 3485, 35, 2900, 2496, 3394, 1518, 3958, 2099, 3784, 2348, 2096, 3391, 828, 743, 731, 2171, 3708, 3327, 1377, 3961, 2777, 3283, 3022, 268, 2102, 3983, 2126, 3773, 3089, 515, 2407, 2041, 175, 44, 2351, 2862, 2952, 294, 2570, 419, 2089, 3787, 1143, 1437, 1748, 1610, 1550, 698, 1888, 3139, 4067, 2573, 4018, 1546, 1087, 3236, 422, 1956, 927, 3903, 3115, 11, 994, 4022, 1801, 2463, 3790, 2065, 1697, 759, 511, 1744, 790, 2092, 2937, 3569, 1678, 983, 2761, 3205, 2577, 1876, 553, 3864, 76, 1751, 1613, 1070, 3814, 1323, 216, 3583, 1588, 1345, 118, 964, 3699, 4071, 3377, 2203, 1440, 3364, 1562, 1146, 1188, 753, 4007, 262, 1077, 1492, 4048, 2354, 1194, 3304, 3143, 1759, 1917, 2455, 3722, 920, 3610, 168, 1929, 1314, 2865, 237, 297, 1212, 3001, 3402, 1174, 1892, 2419, 414, 4089, 3996, 469, 1668, 3372, 1541, 2996, 2955, 857, 2960, 3160, 178, 885, 2220, 702, 3197, 370, 619, 1662, 3109, 47, 2401, 767, 3884, 2634, 2254, 2044, 2881, 442, 1598, 2232, 1554, 2785, 2058, 3803, 3976, 312, 2410, 1133, 2660, 1507, 227, 2174, 2377, 3064, 1410, 844, 3912, 15, 363, 1840, 3349, 2293, 734, 336, 3125, 3436, 3689, 1854, 3711, 1476, 147, 2135, 22, 3512, 3119, 2628, 3858, 3330, 2342, 474, 1635, 3286, 2534, 3680, 2603, 625, 1575, 30, 726, 2267, 4034, 3907, 1226, 3578, 1673, 163, 2780, 2985, 1380, 672, 2155, 1231, 2544, 491, 1468, 329, 2247, 681, 931, 525, 1152, 3964, 3920, 2729, 1620, 3100, 1396, 2593, 648, 3776, 2183, 1390, 2129, 613, 4001, 1960, 1982, 2513, 2388, 2305, 3592, 4039, 1051, 805, 874, 3941, 3092, 518, 3297, 3518, 2191, 3746, 426, 815, 3834, 400, 2272, 253, 659, 3986, 3762, 3014, 454, 1568, 462, 2792, 2105, 1863, 3417, 3240, 1363, 2828, 376, 1688, 3729, 543, 3025, 2033, 2820, 4094, 1728, 271, 3457, 2742, 2000, 1296, 1091}; +constexpr uint16_t EXP_TABLE_12[] = {1, 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 280, 808, 1400, 3976, 145, 435, 725, 1919, 2433, 2698, 3991, 176, 464, 624, 1680, 2992, 3289, 1378, 4006, 227, 293, 879, 1457, 3795, 892, 1412, 3724, 925, 1191, 3561, 1586, 2646, 3827, 796, 1316, 3948, 445, 711, 1865, 2523, 2660, 3749, 998, 1066, 3198, 1163, 3485, 1710, 3058, 3103, 1064, 3192, 1153, 3459, 1676, 2964, 3253, 1494, 3706, 647, 1929, 2203, 2468, 2789, 3878, 355, 933, 1263, 3377, 1882, 2542, 2619, 3652, 709, 1871, 2513, 2682, 3719, 896, 1152, 3456, 1673, 2971, 3236, 1509, 3631, 632, 1672, 2968, 3233, 1514, 3646, 587, 1757, 2919, 3488, 1769, 2875, 3396, 1989, 2127, 2264, 2401, 2986, 3319, 1296, 3888, 345, 1003, 1085, 3143, 1216, 3392, 1993, 2139, 2276, 2341, 2918, 3491, 1772, 2868, 3413, 2038, 2074, 2087, 2144, 2217, 2546, 2591, 3624, 625, 1683, 2997, 3286, 1395, 3989, 182, 474, 622, 1714, 3030, 3187, 1180, 3492, 1765, 2863, 3448, 1921, 2179, 2444, 2717, 4014, 251, 269, 791, 1337, 3915, 468, 636, 1668, 2956, 3229, 1454, 3826, 799, 1313, 3939, 428, 756, 1820, 2340, 2917, 3494, 1763, 2853, 3430, 1955, 2277, 2342, 2915, 3500, 1789, 2823, 3328, 1801, 2331, 2852, 3429, 1958, 2282, 2359, 2896, 3577, 1538, 2566, 3587, 524, 1556, 2620, 3661, 734, 1890, 2470, 2787, 3884, 381, 903, 1161, 3483, 1700, 3052, 3133, 1102, 3282, 1407, 3969, 138, 414, 674, 2022, 2090, 2167, 2192, 2489, 2754, 3919, 472, 616, 1720, 3016, 3153, 1274, 3342, 1819, 2349, 2942, 3467, 1684, 3004, 3277, 1374, 4066, 47, 113, 147, 437, 735, 1889, 2467, 2796, 3901, 334, 978, 1142, 3226, 1447, 3817, 818, 1366, 4090, 7, 9, 27, 45, 119, 153, 427, 765, 1799, 2313, 2834, 3391, 1864, 2520, 2657, 3754, 1015, 1049, 3115, 1140, 3228, 1453, 3831, 784, 1328, 3920, 505, 523, 1565, 2599, 3680, 681, 2043, 2061, 2078, 2091, 2164, 2197, 2486, 2771, 3964, 397, 663, 1977, 2251, 2388, 3061, 3094, 1075, 3157, 1270, 3354, 1831, 2409, 2994, 3295, 1384, 4024, 193, 323, 965, 1103, 3281, 1402, 3982, 155, 429, 759, 1817, 2347, 2932, 3477, 1718, 3034, 3175, 1184, 3552, 1577, 2683, 3716, 901, 1167, 3473, 1722, 3022, 3163, 1252, 3372, 1917, 2439, 2688, 3977, 146, 438, 730, 1902, 2482, 2783, 3944, 433, 723, 1909, 2463, 2728, 4081, 26, 46, 114, 150, 442, 718, 1874, 2550, 2579, 3644, 589, 1751, 2937, 3458, 1679, 2961, 3258, 1479, 3657, 722, 1910, 2458, 2727, 4064, 41, 123, 141, 407, 697, 1995, 2141, 2286, 2363, 2884, 3525, 1606, 2762, 3927, 496, 528, 1584, 2640, 3833, 770, 1286, 3850, 279, 825, 1355, 4061, 110, 178, 470, 634, 1678, 2962, 3263, 1480, 3672, 737, 1827, 2405, 2982, 3299, 1324, 3956, 405, 703, 1985, 2115, 2252, 2397, 3054, 3131, 1092, 3276, 1373, 4071, 32, 96, 160, 480, 544, 1632, 2720, 4073, 50, 86, 250, 270, 786, 1334, 3930, 487, 553, 1659, 2701, 3998, 171, 509, 519, 1545, 2587, 3620, 613, 1711, 3057, 3098, 1063, 3177, 1202, 3542, 1651, 2709, 4022, 211, 373, 927, 1185, 3555, 1580, 2676, 3733, 950, 1242, 3438, 1979, 2253, 2398, 3051, 3124, 1109, 3327, 1288, 3864, 289, 867, 1445, 3823, 824, 1352, 4056, 97, 163, 485, 559, 1649, 2707, 4028, 205, 343, 1017, 1035, 3101, 1070, 3186, 1183, 3489, 1770, 2878, 3403, 2004, 2172, 2189, 2462, 2731, 4084, 21, 63, 65, 195, 325, 975, 1105, 3315, 1308, 3876, 357, 943, 1265, 3347, 1852, 2372, 3013, 3142, 1219, 3397, 1990, 2122, 2263, 2416, 2969, 3234, 1519, 3633, 602, 1774, 2866, 3423, 2024, 2104, 2113, 2250, 2391, 3056, 3097, 1058, 3174, 1187, 3557, 1574, 2666, 3767, 976, 1136, 3216, 1465, 3787, 852, 1532, 3588, 517, 1551, 2577, 3642, 583, 1737, 2907, 3556, 1573, 2671, 3768, 961, 1091, 3269, 1350, 4042, 87, 249, 267, 797, 1319, 3945, 434, 726, 1914, 2446, 2715, 4004, 229, 303, 881, 1427, 3765, 982, 1146, 3214, 1435, 3757, 1022, 1026, 3078, 1027, 3077, 1030, 3082, 1047, 3129, 1090, 3270, 1347, 4037, 70, 202, 350, 994, 1062, 3178, 1207, 3545, 1634, 2726, 4067, 44, 116, 156, 420, 748, 1844, 2396, 3053, 3134, 1099, 3293, 1390, 4018, 223, 353, 931, 1253, 3375, 1912, 2440, 2705, 4026, 199, 329, 987, 1133, 3255, 1488, 3696, 665, 1963, 2301, 2318, 2843, 3364, 1893, 2479, 2808, 3841, 266, 798, 1314, 3942, 419, 741, 1839, 2417, 2970, 3239, 1504, 3616, 617, 1723, 3021, 3166, 1259, 3389, 1870, 2514, 2687, 3720, 913, 1203, 3541, 1654, 2714, 4007, 224, 288, 864, 1440, 3808, 809, 1403, 3981, 158, 418, 742, 1834, 2430, 2955, 3220, 1461, 3807, 872, 1464, 3784, 849, 1523, 3605, 566, 1626, 2798, 3899, 324, 972, 1108, 3324, 1293, 3863, 304, 848, 1520, 3600, 569, 1611, 2781, 3950, 443, 717, 1879, 2553, 2562, 3599, 536, 1576, 2680, 3713, 906, 1182, 3490, 1775, 2865, 3418, 2023, 2089, 2162, 2207, 2472, 2801, 3866, 295, 873, 1467, 3789, 862, 1506, 3622, 611, 1701, 3055, 3128, 1089, 3267, 1356, 4052, 117, 159, 417, 739, 1829, 2415, 3000, 3265, 1354, 4062, 107, 189, 455, 585, 1755, 2925, 3518, 1739, 2909, 3566, 1595, 2637, 3806, 875, 1469, 3783, 832, 1472, 3648, 713, 1883, 2541, 2622, 3659, 724, 1916, 2436, 2693, 3974, 131, 389, 655, 1937, 2227, 2524, 2669, 3774, 971, 1117, 3303, 1312, 3936, 425, 763, 1805, 2327, 2864, 3417, 2018, 2086, 2147, 2220, 2557, 2574, 3611, 548, 1644, 2740, 4053, 118, 154, 430, 754, 1814, 2362, 2887, 3520, 1609, 2779, 3940, 421, 751, 1841, 2387, 3068, 3085, 1054, 3106, 1135, 3249, 1498, 3694, 699, 1997, 2135, 2288, 2329, 2850, 3439, 1976, 2248, 2385, 3066, 3079, 1024, 3072, 1033, 3099, 1060, 3180, 1213, 3527, 1600, 2752, 3913, 466, 630, 1690, 2990, 3323, 1284, 3852, 285, 807, 1385, 4027, 196, 332, 980, 1148, 3204, 1413, 3727, 920, 1192, 3576, 1537, 2563, 3596, 541, 1575, 2665, 3762, 991, 1121, 3235, 1516, 3636, 597, 1791, 2817, 3338, 1815, 2361, 2882, 3535, 1624, 2792, 3889, 346, 1006, 1074, 3158, 1267, 3349, 1846, 2394, 3047, 3104, 1129, 3259, 1476, 3660, 733, 1895, 2473, 2802, 3871, 296, 888, 1416, 3736, 929, 1251, 3365, 1894, 2474, 2807, 3856, 313, 843, 1501, 3687, 672, 2016, 2080, 2153, 2226, 2527, 2664, 3761, 986, 1134, 3250, 1503, 3681, 682, 2046, 2050, 2063, 2072, 2081, 2154, 2231, 2512, 2681, 3714, 911, 1169, 3507, 1756, 2916, 3493, 1766, 2858, 3447, 1936, 2224, 2521, 2658, 3759, 1016, 1032, 3096, 1057, 3171, 1196, 3572, 1557, 2623, 3656, 721, 1907, 2453, 2742, 4051, 124, 132, 396, 660, 1980, 2244, 2373, 3014, 3139, 1228, 3412, 2037, 2079, 2088, 2161, 2202, 2471, 2784, 3881, 370, 918, 1210, 3534, 1627, 2797, 3902, 331, 989, 1127, 3241, 1522, 3606, 563, 1621, 2815, 3848, 273, 819, 1365, 4095, 8, 24, 40, 120, 136, 408, 680, 2040, 2056, 2065, 2106, 2119, 2240, 2377, 3026, 3199, 1160, 3480, 1697, 3043, 3116, 1149, 3207, 1408, 3712, 905, 1179, 3501, 1790, 2818, 3343, 1816, 2344, 2929, 3482, 1703, 3049, 3122, 1119, 3297, 1322, 3966, 395, 669, 1959, 2281, 2354, 2911, 3560, 1585, 2643, 3836, 781, 1303, 3897, 322, 966, 1098, 3294, 1387, 4029, 206, 338, 1014, 1050, 3118, 1147, 3213, 1438, 3746, 1007, 1073, 3155, 1276, 3332, 1797, 2319, 2840, 3361, 1898, 2494, 2763, 3924, 501, 543, 1569, 2659, 3756, 1021, 1031, 3081, 1042, 3126, 1107, 3317, 1302, 3898, 327, 969, 1115, 3309, 1342, 3906, 463, 593, 1779, 2837, 3382, 1875, 2549, 2582, 3635, 604, 1764, 2860, 3453, 1934, 2194, 2495, 2760, 3921, 506, 526, 1554, 2614, 3667, 764, 1796, 2316, 2845, 3374, 1915, 2445, 2718, 4011, 244, 284, 804, 1388, 4020, 213, 383, 897, 1155, 3461, 1670, 2954, 3223, 1456, 3792, 889, 1419, 3741, 942, 1266, 3350, 1843, 2389, 3062, 3091, 1084, 3140, 1221, 3407, 2008, 2152, 2225, 2522, 2663, 3744, 1001, 1083, 3149, 1246, 3426, 1967, 2289, 2330, 2855, 3424, 1961, 2299, 2308, 2821, 3334, 1795, 2309, 2822, 3331, 1804, 2324, 2869, 3414, 2035, 2069, 2102, 2131, 2300, 2317, 2846, 3371, 1908, 2460, 2733, 4094, 11, 29, 39, 105, 187, 461, 599, 1785, 2827, 3348, 1845, 2399, 3048, 3121, 1114, 3310, 1339, 3917, 478, 610, 1702, 3050, 3127, 1104, 3312, 1305, 3883, 372, 924, 1188, 3564, 1597, 2631, 3776, 841, 1499, 3693, 702, 1986, 2118, 2243, 2380, 3037, 3182, 1211, 3533, 1630, 2786, 3887, 376, 904, 1176, 3496, 1777, 2835, 3388, 1869, 2519, 2672, 3737, 930, 1254, 3370, 1911, 2457, 2722, 4079, 56, 72, 216, 360, 952, 1224, 3416, 2017, 2083, 2156, 2237, 2510, 2651, 3812, 805, 1391, 4017, 218, 366, 946, 1238, 3450, 1927, 2185, 2450, 2751, 4040, 81, 243, 277, 831, 1345, 4035, 76, 212, 380, 900, 1164, 3476, 1717, 3039, 3176, 1201, 3539, 1660, 2692, 3973, 134, 394, 670, 1954, 2278, 2339, 2924, 3517, 1742, 2898, 3583, 1544, 2584, 3617, 618, 1726, 3010, 3151, 1240, 3432, 1969, 2259, 2428, 2957, 3230, 1451, 3837, 782, 1298, 3894, 339, 1013, 1055, 3105, 1130, 3262, 1483, 3677, 750, 1842, 2390, 3059, 3100, 1069, 3191, 1168, 3504, 1753, 2923, 3508, 1749, 2943, 3464, 1681, 2995, 3292, 1389, 4023, 208, 368, 912, 1200, 3536, 1657, 2699, 3988, 181, 479, 609, 1699, 3045, 3110, 1123, 3237, 1510, 3626, 631, 1689, 2987, 3316, 1301, 3903, 328, 984, 1128, 3256, 1473, 3651, 716, 1876, 2556, 2573, 3614, 555, 1661, 2695, 3968, 137, 411, 685, 2039, 2073, 2082, 2159, 2232, 2497, 2634, 3799, 880, 1424, 3760, 985, 1131, 3261, 1486, 3666, 767, 1793, 2307, 2828, 3357, 1838, 2418, 2975, 3240, 1521, 3603, 572, 1604, 2764, 3933, 494, 562, 1622, 2810, 3847, 256, 768, 1280, 3840, 265, 795, 1325, 3959, 400, 688, 2000, 2160, 2201, 2466, 2799, 3896, 321, 963, 1093, 3279, 1368, 4072, 49, 83, 245, 287, 801, 1379, 4005, 230, 298, 894, 1410, 3718, 899, 1157, 3471, 1688, 2984, 3313, 1306, 3886, 379, 909, 1175, 3513, 1730, 2886, 3523, 1612, 2772, 3957, 406, 698, 1998, 2130, 2303, 2312, 2833, 3386, 1863, 2505, 2642, 3839, 776, 1304, 3880, 369, 915, 1205, 3551, 1640, 2744, 4033, 74, 222, 354, 934, 1258, 3390, 1867, 2525, 2670, 3771, 964, 1100, 3284, 1397, 3999, 168, 504, 520, 1560, 2600, 3697, 666, 1966, 2290, 2335, 2856, 3441, 1946, 2222, 2555, 2564, 3589, 518, 1546, 2590, 3627, 628, 1692, 2980, 3301, 1318, 3946, 439, 729, 1899, 2493, 2766, 3931, 484, 556, 1652, 2716, 4013, 254, 258, 774, 1290, 3870, 299, 893, 1415, 3721, 914, 1206, 3546, 1639, 2729, 4082, 31, 33, 99, 165, 495, 561, 1619, 2805, 3862, 307, 853, 1535, 3585, 522, 1566, 2594, 3695, 696, 1992, 2136, 2273, 2346, 2935, 3472, 1721, 3019, 3156, 1269, 3359, 1832, 2424, 2945, 3210, 1431, 3769, 962, 1094, 3274, 1367, 4089, 2, 6, 10, 30, 34, 102, 170, 510, 514, 1542, 2570, 3607, 560, 1616, 2800, 3865, 290, 870, 1450, 3838, 779, 1309, 3879, 352, 928, 1248, 3360, 1897, 2491, 2756, 3909, 454, 586, 1758, 2914, 3503, 1784, 2824, 3345, 1850, 2382, 3035, 3172, 1189, 3567, 1592, 2632, 3793, 890, 1422, 3730, 959, 1217, 3395, 1996, 2132, 2293, 2326, 2867, 3420, 2029, 2103, 2128, 2297, 2306, 2831, 3352, 1825, 2403, 2988, 3325, 1294, 3858, 319, 833, 1475, 3653, 710, 1866, 2526, 2667, 3764, 981, 1151, 3201, 1418, 3742, 939, 1277, 3335, 1792, 2304, 2825, 3346, 1855, 2369, 3018, 3159, 1264, 3344, 1849, 2379, 3028, 3189, 1174, 3514, 1735, 2889, 3538, 1663, 2689, 3978, 151, 441, 715, 1885, 2535, 2592, 3689, 690, 2006, 2170, 2183, 2432, 2697, 3986, 191, 449, 579, 1733, 2895, 3544, 1633, 2723, 4076, 61, 71, 201, 347, 1005, 1079, 3161, 1250, 3366, 1891, 2469, 2790, 3875, 364, 948, 1244, 3428, 1957, 2287, 2360, 2881, 3530, 1623, 2809, 3842, 271, 785, 1331, 3925, 502, 538, 1582, 2674, 3743, 936, 1272, 3336, 1809, 2355, 2908, 3565, 1598, 2626, 3791, 856, 1512, 3640, 577, 1731, 2885, 3526, 1603, 2757, 3910, 451, 581, 1743, 2897, 3578, 1543, 2569, 3602, 575, 1601, 2755, 3916, 477, 615, 1705, 3067, 3076, 1029, 3087, 1048, 3112, 1137, 3219, 1468, 3780, 837, 1487, 3665, 762, 1806, 2322, 2879, 3400, 2001, 2163, 2204, 2477, 2814, 3851, 276, 828, 1348, 4044, 93, 231, 297, 891, 1421, 3735, 944, 1232, 3440, 1945, 2219, 2548, 2581, 3638, 595, 1781, 2847, 3368, 1905, 2451, 2748, 4045, 94, 226, 294, 874, 1470, 3778, 847, 1489, 3699, 668, 1956, 2284, 2365, 2894, 3547, 1636, 2732, 4093, 14, 18, 54, 90, 238, 306, 854, 1530, 3598, 539, 1581, 2679, 3728, 953, 1227, 3421, 2030, 2098, 2143, 2280, 2353, 2906, 3559, 1568, 2656, 3753, 1010, 1046, 3130, 1095, 3273, 1362, 4086, 19, 53, 95, 225, 291, 869, 1455, 3825, 794, 1326, 3954, 415, 673, 2019, 2085, 2150, 2211, 2540, 2621, 3662, 731, 1901, 2487, 2768, 3961, 386, 646, 1930, 2206, 2475, 2804, 3861, 310, 858, 1518, 3634, 607, 1761, 2851, 3436, 1981, 2247, 2368, 3017, 3154, 1279, 3329, 1802, 2334, 2859, 3444, 1941, 2239, 2504, 2641, 3834, 775, 1289, 3867, 292, 876, 1460, 3804, 877, 1463, 3801, 866, 1446, 3818, 823, 1369, 4075, 52, 92, 228, 300, 884, 1436, 3748, 997, 1071, 3185, 1178, 3502, 1787, 2829, 3358, 1835, 2429, 2958, 3227, 1444, 3820, 829, 1351, 4041, 82, 246, 282, 814, 1394, 3990, 179, 469, 639, 1665, 2947, 3212, 1437, 3751, 992, 1056, 3168, 1193, 3579, 1540, 2572, 3613, 558, 1650, 2710, 4019, 220, 356, 940, 1268, 3356, 1837, 2423, 2960, 3257, 1474, 3654, 707, 1861, 2511, 2648, 3809, 810, 1406, 3970, 143, 401, 691, 2005, 2175, 2184, 2449, 2746, 4039, 64, 192, 320, 960, 1088, 3264, 1353, 4059, 100, 172, 500, 540, 1572, 2668, 3773, 974, 1106, 3318, 1299, 3893, 342, 1018, 1038, 3090, 1087, 3137, 1226, 3422, 2027, 2109, 2126, 2267, 2404, 2981, 3302, 1315, 3941, 422, 746, 1854, 2370, 3023, 3160, 1249, 3363, 1900, 2484, 2773, 3958, 403, 693, 2015, 2145, 2218, 2551, 2576, 3641, 578, 1734, 2890, 3543, 1648, 2704, 4025, 194, 326, 970, 1118, 3298, 1327, 3953, 410, 686, 2034, 2070, 2099, 2140, 2285, 2366, 2891, 3540, 1653, 2719, 4008, 241, 275, 821, 1375, 4065, 42, 126, 130, 390, 650, 1950, 2210, 2543, 2616, 3649, 714, 1886, 2530, 2607, 3704, 641, 1923, 2181, 2438, 2691, 3980, 157, 423, 745, 1851, 2381, 3038, 3179, 1204, 3548, 1645, 2743, 4048, 121, 139, 413, 679, 2025, 2107, 2116, 2245, 2374, 3011, 3148, 1245, 3431, 1952, 2272, 2345, 2930, 3487, 1704, 3064, 3073, 1034, 3102, 1067, 3197, 1166, 3474, 1727, 3009, 3146, 1239, 3449, 1922, 2182, 2435, 2700, 3997, 174, 498, 534, 1594, 2638, 3803, 868, 1452, 3828, 789, 1343, 3905, 458, 606, 1762, 2854, 3427, 1964, 2292, 2325, 2870, 3411, 2044, 2052, 2053, 2054, 2051, 2060, 2077, 2094, 2171, 2180, 2437, 2694, 3971, 140, 404, 700, 1988, 2124, 2269, 2414, 3003, 3268, 1349, 4047, 88, 232, 312, 840, 1496, 3688, 689, 2003, 2165, 2198, 2483, 2780, 3949, 446, 706, 1862, 2506, 2647, 3824, 793, 1323, 3965, 398, 658, 1974, 2266, 2407, 2976, 3305, 1330, 3926, 499, 533, 1599, 2625, 3786, 855, 1529, 3595, 532, 1596, 2628, 3781, 838, 1482, 3678, 747, 1853, 2375, 3008, 3145, 1234, 3446, 1939, 2229, 2518, 2675, 3740, 941, 1271, 3353, 1826, 2406, 2979, 3308, 1341, 3911, 448, 576, 1728, 2880, 3529, 1618, 2806, 3859, 316, 836, 1484, 3668, 757, 1823, 2337, 2922, 3511, 1744, 2928, 3481, 1698, 3046, 3107, 1132, 3252, 1493, 3711, 648, 1944, 2216, 2545, 2586, 3623, 608, 1696, 3040, 3113, 1138, 3222, 1459, 3797, 886, 1434, 3758, 1019, 1037, 3095, 1072, 3152, 1273, 3339, 1812, 2364, 2893, 3550, 1643, 2749, 4046, 91, 237, 311, 857, 1515, 3645, 590, 1746, 2934, 3475, 1724, 3012, 3141, 1222, 3402, 2007, 2169, 2178, 2447, 2712, 4001, 234, 318, 834, 1478, 3658, 727, 1913, 2443, 2708, 4021, 214, 378, 910, 1170, 3510, 1747, 2933, 3478, 1715, 3029, 3190, 1171, 3509, 1750, 2938, 3463, 1664, 2944, 3209, 1426, 3766, 979, 1141, 3231, 1448, 3832, 769, 1283, 3845, 262, 778, 1310, 3874, 367, 945, 1235, 3445, 1942, 2234, 2503, 2624, 3785, 850, 1526, 3610, 551, 1641, 2747, 4036, 69, 207, 337, 1011, 1045, 3135, 1096, 3288, 1377, 4003, 236, 308, 860, 1508, 3628, 637, 1671, 2953, 3218, 1471, 3777, 842, 1502, 3682, 687, 2033, 2067, 2108, 2125, 2270, 2411, 2996, 3285, 1398, 3994, 167, 489, 571, 1613, 2775, 3952, 409, 683, 2045, 2055, 2048, 2057, 2066, 2111, 2120, 2257, 2426, 2951, 3200, 1417, 3739, 932, 1260, 3380, 1877, 2559, 2568, 3601, 570, 1614, 2770, 3967, 392, 664, 1960, 2296, 2305, 2826, 3351, 1840, 2384, 3065, 3074, 1039, 3089, 1082, 3150, 1243, 3437, 1982, 2242, 2383, 3032, 3169, 1194, 3582, 1547, 2589, 3630, 635, 1677, 2967, 3248, 1497, 3691, 692, 2012, 2148, 2213, 2534, 2595, 3692, 701, 1991, 2121, 2258, 2431, 2952, 3217, 1466, 3790, 859, 1517, 3639, 592, 1776, 2832, 3385, 1858, 2502, 2627, 3788, 861, 1511, 3625, 626, 1686, 3002, 3271, 1344, 4032, 73, 219, 365, 951, 1241, 3435, 1972, 2268, 2413, 3006, 3275, 1364, 4092, 13, 23, 57, 75, 221, 359, 937, 1275, 3341, 1822, 2338, 2927, 3512, 1729, 2883, 3532, 1629, 2791, 3872, 361, 955, 1229, 3415, 2032, 2064, 2105, 2114, 2255, 2392, 3041, 3114, 1143, 3225, 1442, 3814, 803, 1381, 4015, 248, 264, 792, 1320, 3960, 385, 643, 1925, 2191, 2456, 2721, 4074, 55, 89, 235, 317, 839, 1481, 3675, 740, 1836, 2420, 2965, 3254, 1491, 3701, 662, 1978, 2254, 2395, 3044, 3109, 1126, 3242, 1527, 3609, 546, 1638, 2730, 4087, 16, 48, 80, 240, 272, 816, 1360, 4080, 25, 43, 125, 135, 393, 667, 1965, 2295, 2320, 2873, 3394, 1999, 2129, 2298, 2311, 2816, 3337, 1810, 2358, 2899, 3580, 1549, 2583, 3632, 601, 1771, 2877, 3406, 2011, 2157, 2238, 2507, 2644, 3829, 790, 1338, 3918, 475, 621, 1719, 3033, 3170, 1199, 3569, 1562, 2606, 3707, 644, 1932, 2196, 2485, 2774, 3955, 412, 676, 2028, 2100, 2133, 2294, 2323, 2876, 3405, 2014, 2146, 2223, 2552, 2561, 3594, 535, 1593, 2635, 3796, 885, 1439, 3745, 1002, 1086, 3138, 1231, 3409, 2042, 2062, 2075, 2084, 2149, 2214, 2531, 2604, 3709, 654, 1938, 2230, 2515, 2684, 3725, 926, 1186, 3558, 1571, 2661, 3750, 995, 1061, 3183, 1208, 3528, 1617, 2803, 3868, 301, 887, 1433, 3755, 1012, 1052, 3108, 1125, 3247, 1528, 3592, 529, 1587, 2645, 3830, 787, 1333, 3935, 488, 568, 1608, 2776, 3937, 426, 766, 1794, 2310, 2819, 3340, 1821, 2343, 2912, 3497, 1778, 2838, 3379, 1884, 2532, 2597, 3686, 675, 2021, 2095, 2168, 2177, 2442, 2711, 4016, 217, 363, 957, 1223, 3401, 2002, 2166, 2195, 2492, 2765, 3934, 491, 573, 1607, 2761, 3922, 511, 513, 1539, 2565, 3590, 515, 1541, 2575, 3608, 545, 1635, 2725, 4070, 35, 101, 175, 497, 531, 1589, 2655, 3816, 817, 1363, 4085, 22, 58, 78, 210, 374, 922, 1198, 3570, 1567, 2593, 3690, 695, 2009, 2155, 2228, 2517, 2678, 3731, 956, 1220, 3404, 2013, 2151, 2208, 2537, 2610, 3679, 744, 1848, 2376, 3025, 3194, 1159, 3465, 1682, 2998, 3283, 1404, 3972, 133, 399, 657, 1971, 2261, 2422, 2963, 3260, 1485, 3671, 752, 1808, 2352, 2905, 3554, 1583, 2673, 3738, 935, 1257, 3387, 1860, 2508, 2653, 3822, 827, 1357, 4055, 112, 144, 432, 720, 1904, 2448, 2745, 4034, 79, 209, 371, 917, 1215, 3521, 1610, 2782, 3947, 436, 732, 1892, 2476, 2813, 3854, 283, 813, 1399, 3993, 162, 486, 554, 1662, 2690, 3983, 152, 424, 760, 1800, 2328, 2849, 3434, 1975, 2265, 2402, 2991, 3320, 1281, 3843, 268, 788, 1340, 3908, 453, 591, 1745, 2931, 3484, 1709, 3063, 3088, 1081, 3147, 1236, 3452, 1933, 2199, 2480, 2777, 3938, 431, 753, 1811, 2357, 2902, 3571, 1564, 2596, 3685, 678, 2026, 2110, 2123, 2260, 2421, 2966, 3251, 1500, 3684, 677, 2031, 2097, 2138, 2279, 2336, 2921, 3506, 1759, 2913, 3498, 1783, 2841, 3362, 1903, 2481, 2778, 3943, 416, 736, 1824, 2400, 2985, 3314, 1311, 3873, 362, 958, 1218, 3398, 1987, 2117, 2246, 2371, 3020, 3165, 1262, 3378, 1887, 2529, 2602, 3703, 656, 1968, 2256, 2425, 2946, 3215, 1432, 3752, 1009, 1043, 3125, 1110, 3322, 1287, 3849, 274, 822, 1370, 4078, 59, 77, 215, 377, 907, 1181, 3495, 1760, 2848, 3433, 1970, 2262, 2419, 2972, 3245, 1534, 3586, 527, 1553, 2611, 3676, 749, 1847, 2393, 3042, 3119, 1144, 3208, 1425, 3763, 988, 1124, 3244, 1533, 3591, 512, 1536, 2560, 3593, 530, 1590, 2650, 3815, 800, 1376, 4000, 233, 315, 845, 1495, 3705, 642, 1926, 2186, 2455, 2736, 4057, 98, 166, 490, 574, 1602, 2758, 3907, 460, 596, 1788, 2820, 3333, 1798, 2314, 2839, 3376, 1881, 2539, 2612, 3669, 758, 1818, 2350, 2939, 3460, 1669, 2959, 3224, 1441, 3811, 812, 1396, 3996, 173, 503, 537, 1579, 2685, 3726, 923, 1197, 3575, 1552, 2608, 3673, 738, 1830, 2410, 2999, 3280, 1401, 3979, 148, 444, 708, 1868, 2516, 2677, 3734, 947, 1237, 3455, 1928, 2200, 2465, 2794, 3895, 336, 1008, 1040, 3120, 1113, 3307, 1332, 3932, 493, 567, 1625, 2795, 3892, 341, 1023, 1025, 3075, 1036, 3092, 1077, 3167, 1256, 3384, 1857, 2499, 2636, 3805, 878, 1458, 3798, 883, 1429, 3775, 968, 1112, 3304, 1329, 3923, 508, 516, 1548, 2580, 3637, 598, 1786, 2830, 3355, 1828, 2412, 3005, 3278, 1371, 4077, 62, 66, 198, 330, 990, 1122, 3238, 1507, 3621, 614, 1706, 3070, 3083, 1044, 3132, 1101, 3287, 1392, 3984, 185, 459, 605, 1767, 2857, 3442, 1951, 2209, 2538, 2615, 3664, 761, 1803, 2333, 2862, 3451, 1924, 2188, 2461, 2734, 4091, 4, 12, 20, 60, 68, 204, 340, 1020, 1028, 3084, 1053, 3111, 1120, 3232, 1513, 3643, 580, 1740, 2900, 3573, 1558, 2618, 3655, 704, 1856, 2496, 2633, 3794, 895, 1409, 3715, 908, 1172, 3516, 1741, 2903, 3568, 1561, 2603, 3700, 661, 1983, 2241, 2378, 3031, 3184, 1177, 3499, 1780, 2844, 3373, 1918, 2434, 2703, 3992, 161, 483, 549, 1647, 2737, 4058, 103, 169, 507, 525, 1559, 2617, 3650, 719, 1873, 2547, 2588, 3629, 638, 1666, 2950, 3203, 1420, 3732, 949, 1247, 3425, 1962, 2302, 2315, 2836, 3381, 1878, 2554, 2567, 3584, 521, 1563, 2605, 3710, 651, 1949, 2215, 2528, 2601, 3698, 671, 1953, 2275, 2348, 2941, 3470, 1691, 2989, 3326, 1291, 3869, 302, 882, 1430, 3770, 967, 1097, 3291, 1380, 4012, 253, 263, 777, 1307, 3885, 382, 898, 1158, 3466, 1687, 3001, 3266, 1359, 4049, 122, 142, 402, 694, 2010, 2158, 2235, 2500, 2629, 3782, 835, 1477, 3663, 728, 1896, 2488, 2753, 3914, 471, 633, 1675, 2973, 3246, 1531, 3597, 542, 1570, 2662, 3747, 1004, 1076, 3164, 1261, 3383, 1872, 2544, 2585, 3618, 623, 1713, 3027, 3196, 1165, 3479, 1712, 3024, 3193, 1154, 3462, 1667, 2949, 3206, 1411, 3717, 902, 1162, 3486, 1707, 3069, 3086, 1051, 3117, 1150, 3202, 1423, 3729, 954, 1230, 3410, 2047, 2049, 2058, 2071, 2096, 2137, 2274, 2351, 2936, 3457, 1674, 2974, 3243, 1524, 3612, 557, 1655, 2713, 4002, 239, 305, 851, 1525, 3615, 552, 1656, 2696, 3985, 186, 462, 594, 1782, 2842, 3367, 1888, 2464, 2793, 3890, 351, 993, 1059, 3173, 1190, 3562, 1591, 2649, 3810, 815, 1393, 3987, 188, 452, 588, 1748, 2940, 3469, 1694, 2978, 3311, 1336, 3912, 465, 627, 1685, 3007, 3272, 1361, 4083, 28, 36, 108, 180, 476, 612, 1708, 3060, 3093, 1078, 3162, 1255, 3369, 1906, 2454, 2739, 4060, 109, 183, 473, 619, 1725, 3015, 3136, 1225, 3419, 2020, 2092, 2173, 2190, 2459, 2724, 4069, 38, 106, 190, 450, 582, 1738, 2910, 3563, 1588, 2652, 3821, 830, 1346, 4038, 67, 197, 335, 977, 1139, 3221, 1462, 3802, 871, 1449, 3835, 772, 1292, 3860, 309, 863, 1505, 3619, 620, 1716, 3036, 3181, 1214, 3522, 1615, 2769, 3962, 391, 649, 1947, 2221, 2558, 2571, 3604, 565, 1631, 2785, 3882, 375, 921, 1195, 3581, 1550, 2578, 3647, 584, 1752, 2920, 3505, 1754, 2926, 3515, 1732, 2892, 3549, 1646, 2738, 4063, 104, 184, 456, 600, 1768, 2872, 3393, 1994, 2142, 2283, 2356, 2901, 3574, 1555, 2613, 3670, 755, 1813, 2367, 2888, 3537, 1658, 2702, 3995, 164, 492, 564, 1628, 2788, 3877, 358, 938, 1278, 3330, 1807, 2321, 2874, 3399, 1984, 2112, 2249, 2386, 3071, 3080, 1041, 3123, 1116, 3300, 1317, 3951, 440, 712, 1880, 2536, 2609, 3674, 743, 1833, 2427, 2948, 3205, 1414, 3722, 919, 1209, 3531, 1620, 2812, 3853, 286, 802, 1382, 4010, 247, 281, 811, 1405, 3975, 128, 384, 640, 1920, 2176, 2441, 2706, 4031, 200, 344, 1000, 1080, 3144, 1233, 3443, 1948, 2212, 2533, 2598, 3683, 684, 2036, 2076, 2093, 2174, 2187, 2452, 2741, 4054, 115, 149, 447, 705, 1859, 2501, 2630, 3779, 844, 1492, 3708, 653, 1943, 2233, 2498, 2639, 3800, 865, 1443, 3813, 806, 1386, 4030, 203, 349, 999, 1065, 3195, 1156, 3468, 1693, 2983, 3296, 1321, 3963, 388, 652, 1940, 2236, 2509, 2654, 3819, 820, 1372, 4068, 37, 111, 177, 467, 629, 1695, 2977, 3306, 1335, 3929, 482, 550, 1642, 2750, 4043, 84, 252, 260, 780, 1300, 3900, 333, 983, 1145, 3211, 1428, 3772, 973, 1111, 3321, 1282, 3846, 259, 773, 1295, 3857, 314, 846, 1490, 3702, 659, 1973, 2271, 2408, 2993, 3290, 1383, 4009, 242, 278, 826, 1358, 4050, 127, 129, 387, 645, 1935, 2193, 2490, 2759, 3904, 457, 603, 1773, 2871, 3408, 2041, 2059, 2068, 2101, 2134, 2291, 2332, 2861, 3454, 1931, 2205, 2478, 2811, 3844, 261, 783, 1297, 3891, 348, 996, 1068, 3188, 1173, 3519, 1736, 2904, 3553, 1578, 2686, 3723, 916, 1212, 3524, 1605, 2767, 3928, 481, 547, 1637, 2735, 4088, 1}; +typedef Field Field12; + +// 13 bit field +typedef RecLinTrans StatTable13; +constexpr StatTable13 QRT_TABLE_13({3324, 5376, 5378, 898, 5382, 5276, 906, 280, 5398, 0, 5308, 4110, 970}); +constexpr uint16_t LOG_TABLE_13[] = {8191, 0, 1, 934, 2, 1868, 935, 6336, 3, 7270, 1869, 490, 936, 93, 6337, 2802, 4, 3736, 7271, 6206, 1870, 4481, 491, 1027, 937, 4508, 94, 13, 6338, 1424, 2803, 6263, 5, 7197, 3737, 6429, 7272, 3439, 6207, 2358, 1871, 5081, 4482, 5442, 492, 947, 1028, 5013, 938, 6826, 4509, 4670, 95, 7140, 14, 3034, 6339, 1961, 1425, 7477, 2804, 6574, 6264, 5415, 6, 6349, 7198, 5963, 3738, 980, 6430, 7508, 7273, 1407, 3440, 2895, 6208, 220, 2359, 2653, 1872, 186, 5082, 7760, 4483, 5604, 5443, 5466, 493, 3968, 948, 1523, 1029, 4408, 5014, 8074, 939, 290, 6827, 8131, 4510, 7363, 4671, 5707, 96, 3292, 7141, 2626, 15, 7865, 3035, 4373, 6340, 5947, 1962, 2379, 1426, 5188, 7478, 1881, 2805, 4351, 6575, 6015, 6265, 6376, 5416, 583, 7, 1517, 6350, 2335, 7199, 1179, 5964, 7310, 3739, 5036, 981, 5285, 6431, 6949, 7509, 8161, 7274, 5791, 1408, 6881, 3441, 3313, 2896, 4971, 6209, 2815, 221, 6356, 2360, 6477, 2654, 6122, 1873, 5622, 187, 1224, 5083, 874, 7761, 7099, 4484, 6641, 5605, 754, 5444, 6696, 5467, 106, 494, 5307, 3969, 4719, 949, 4601, 1524, 608, 1030, 441, 4409, 4226, 5015, 3560, 8075, 5748, 940, 6689, 291, 7283, 6828, 6897, 8132, 6299, 4511, 251, 7364, 322, 4672, 3158, 5708, 1914, 97, 3587, 3293, 4873, 7142, 6317, 2627, 1154, 16, 6753, 7866, 2341, 3036, 3829, 4374, 3226, 6341, 817, 5948, 4998, 1963, 3914, 2380, 5342, 1427, 4574, 5189, 4902, 7479, 2457, 1882, 7527, 2806, 7928, 4352, 1120, 6576, 503, 6016, 832, 6266, 6400, 6377, 1584, 5417, 645, 584, 6538, 8, 7472, 1518, 6010, 6351, 4221, 2336, 1579, 7200, 5503, 1180, 7334, 5965, 2518, 7311, 7570, 3740, 771, 5037, 671, 982, 2054, 5286, 2580, 6432, 1766, 6950, 7205, 7510, 4122, 8162, 1437, 7275, 6667, 5792, 1751, 1409, 5932, 6882, 6626, 3442, 6276, 3314, 1978, 2897, 298, 4972, 4848, 6210, 270, 2816, 5571, 222, 3852, 6357, 3391, 2361, 1083, 6478, 5508, 2655, 5836, 6123, 4072, 1874, 825, 5623, 7623, 188, 26, 1225, 3929, 5084, 7233, 875, 3333, 7762, 2751, 7100, 7831, 4485, 2848, 6642, 3127, 5606, 4335, 755, 4092, 5445, 524, 6697, 1185, 5468, 1256, 107, 4139, 495, 4160, 5308, 4053, 3970, 2130, 4720, 4763, 950, 3193, 4602, 7687, 1525, 3275, 609, 2496, 1031, 1389, 442, 4521, 4410, 5807, 4227, 5630, 5016, 2088, 3561, 7339, 8076, 6919, 5749, 7251, 941, 7859, 6690, 2451, 292, 3269, 7284, 792, 6829, 53, 6898, 377, 8133, 2874, 6300, 2113, 4512, 904, 252, 2553, 7365, 7967, 323, 7883, 4673, 3532, 3159, 5970, 5709, 6219, 1915, 5357, 98, 7056, 3588, 3056, 3294, 3611, 4874, 7411, 7143, 1651, 6318, 3749, 2628, 7290, 1155, 7064, 17, 3076, 6754, 6725, 7867, 7815, 2342, 6522, 3037, 5905, 3830, 2523, 4375, 4303, 3227, 4247, 6342, 6682, 818, 6675, 5949, 5174, 4999, 4494, 1964, 4108, 3915, 1375, 2381, 5160, 5343, 1637, 1428, 4278, 4575, 6241, 5190, 5653, 4903, 1059, 7480, 1542, 2458, 7316, 1883, 1342, 7528, 5535, 2807, 3524, 7929, 6556, 4353, 2158, 1121, 3708, 6577, 8033, 504, 5106, 6017, 798, 833, 1808, 6267, 1040, 6401, 2395, 6378, 4168, 1585, 7630, 5418, 8007, 646, 7575, 585, 1688, 6539, 7743, 9, 486, 7473, 5438, 1519, 2891, 6011, 2622, 6352, 5281, 4222, 750, 2337, 318, 1580, 4898, 7201, 7330, 5504, 1974, 1181, 3329, 7335, 7683, 5966, 373, 2519, 3745, 7312, 1371, 7571, 5102, 3741, 746, 772, 4458, 5038, 7490, 672, 2472, 983, 4642, 2055, 4462, 5287, 6835, 2581, 3092, 6433, 2742, 1767, 2696, 6951, 2013, 7206, 1732, 7511, 3018, 4123, 776, 8163, 6040, 1438, 1454, 7276, 5956, 6668, 7616, 5793, 7609, 1752, 4834, 1410, 5428, 5933, 7494, 6883, 1106, 6627, 6108, 3443, 2571, 6277, 3794, 3315, 4444, 1979, 6094, 2898, 2003, 299, 5042, 4973, 2309, 4849, 5255, 6211, 6469, 271, 1303, 2817, 3948, 5572, 2276, 223, 2923, 3853, 2476, 6358, 59, 3392, 2933, 2362, 6658, 1084, 5212, 6479, 7175, 5509, 195, 2656, 1993, 5837, 676, 6124, 1556, 4073, 6587, 1875, 3028, 826, 602, 5624, 3385, 7624, 6516, 189, 1726, 27, 4646, 1226, 5672, 3930, 4203, 5085, 3047, 7234, 1897, 876, 2417, 3334, 3808, 7763, 7937, 2752, 987, 7101, 1311, 7832, 2719, 4486, 6291, 2849, 5229, 6643, 1356, 3128, 7153, 5607, 3143, 4336, 4466, 756, 6904, 4093, 3596, 5446, 7958, 525, 1838, 6698, 3487, 1186, 4652, 5469, 626, 1257, 2059, 108, 2202, 4140, 710, 496, 5181, 4161, 5800, 5309, 7168, 4054, 5237, 3971, 5549, 2131, 6839, 4721, 3457, 4764, 4937, 951, 1628, 3194, 4010, 4603, 7659, 7688, 6073, 1526, 7456, 3276, 5291, 610, 6453, 2497, 558, 1032, 7920, 1390, 7990, 443, 3990, 4522, 1470, 4411, 154, 5808, 3096, 4228, 383, 5631, 4545, 5017, 7998, 2089, 6981, 3562, 5316, 7340, 33, 8077, 5728, 6920, 2585, 5750, 4683, 7252, 7542, 942, 88, 7860, 215, 6691, 6944, 2452, 3153, 293, 2513, 3270, 2746, 7285, 2869, 793, 5155, 6830, 313, 54, 1101, 6899, 5667, 378, 3452, 8134, 2864, 2875, 6437, 6301, 77, 2114, 4287, 4513, 2371, 905, 5204, 253, 1500, 2554, 5056, 7366, 1049, 7968, 2700, 324, 8139, 7884, 6777, 4674, 636, 3533, 1705, 3160, 1605, 5971, 5678, 5710, 3514, 6220, 1771, 1916, 3893, 5358, 2988, 99, 5006, 7057, 4841, 3589, 3085, 3057, 6770, 3295, 4043, 3612, 2017, 4875, 6442, 7412, 4917, 7144, 7090, 1652, 1204, 6319, 6505, 3750, 6056, 2629, 4325, 7291, 6955, 1156, 7947, 7065, 4786, 18, 972, 3077, 7601, 6755, 2685, 6726, 3767, 7868, 7560, 7816, 1736, 2343, 2880, 6523, 6866, 3038, 5782, 5906, 913, 3831, 5244, 2524, 1232, 4376, 1073, 4304, 7210, 3228, 2912, 4248, 3661, 6343, 8185, 6683, 1511, 819, 7466, 6676, 7853, 5950, 480, 5175, 3022, 5000, 82, 4495, 8179, 1965, 6197, 4109, 2323, 3916, 5455, 1376, 4589, 2382, 6564, 5161, 7515, 5344, 279, 1638, 6741, 1429, 6255, 4279, 5094, 4576, 4987, 6242, 1330, 5191, 5697, 5654, 780, 4904, 6306, 1060, 3064, 7481, 3430, 1543, 5559, 2459, 8150, 7317, 4209, 1884, 176, 1343, 4127, 7529, 430, 5536, 3181, 2808, 4501, 3525, 1759, 7930, 366, 6557, 2857, 4354, 4863, 2159, 6044, 1122, 4292, 3709, 960, 6578, 574, 8034, 4622, 505, 3697, 5107, 3685, 6018, 3904, 799, 8167, 834, 4267, 1809, 164, 6268, 5073, 1041, 4634, 6402, 3116, 2396, 2190, 6379, 5738, 4169, 1458, 1586, 2119, 7631, 1616, 5419, 1398, 8008, 3782, 647, 4061, 7576, 3936, 586, 5026, 1689, 1442, 6540, 5492, 7744, 5269, 10, 6203, 487, 931, 7474, 4667, 5439, 6426, 1520, 7757, 2892, 5960, 6012, 2376, 2623, 8128, 6353, 6878, 5282, 2332, 4223, 4716, 751, 1221, 2338, 4870, 319, 7280, 1581, 1117, 4899, 4995, 7202, 668, 7331, 6007, 5505, 5568, 1975, 1748, 1182, 3124, 3330, 7620, 7336, 4518, 7684, 4050, 5967, 2550, 374, 2448, 2520, 6722, 3746, 3053, 7313, 6238, 1372, 6672, 7572, 2392, 5103, 6553, 3742, 1971, 747, 5435, 773, 2693, 4459, 4455, 5039, 3791, 7491, 7613, 673, 5209, 2473, 1300, 984, 1894, 4643, 599, 2056, 1835, 4463, 5226, 5288, 4007, 6836, 5797, 2582, 6978, 3093, 7987, 6434, 1098, 2743, 212, 1768, 1702, 2697, 5201, 6952, 1201, 2014, 4838, 7207, 910, 1733, 7598, 7512, 2320, 3019, 1508, 4124, 5556, 777, 5091, 8164, 4619, 6041, 1756, 1439, 3779, 1455, 4631, 7277, 2329, 5957, 928, 6669, 2445, 7617, 6004, 5794, 596, 7610, 5432, 1753, 1505, 4835, 209, 1411, 922, 5429, 925, 5934, 7128, 7495, 1016, 6884, 4361, 1107, 1414, 6628, 3956, 6109, 7186, 3444, 7675, 2572, 1019, 6278, 1244, 3795, 1213, 3316, 1567, 4445, 7498, 1980, 258, 6095, 3302, 2899, 6713, 2004, 7131, 300, 3257, 5043, 1903, 4974, 5523, 2310, 5937, 4850, 8021, 5256, 6389, 6212, 4115, 6470, 1417, 272, 70, 1304, 1364, 2818, 3673, 3949, 1110, 5573, 5061, 2277, 1677, 224, 7589, 2924, 4364, 3854, 6493, 2477, 7400, 6359, 5143, 60, 6887, 3393, 3502, 2934, 893, 2363, 738, 6659, 7189, 1085, 6028, 5213, 660, 6480, 2264, 7176, 6112, 5510, 2559, 196, 5921, 2657, 3998, 1994, 3959, 5838, 3978, 677, 7240, 6125, 698, 1557, 6631, 4074, 1714, 6588, 7222, 1876, 5461, 3029, 1022, 827, 1149, 603, 4966, 5625, 4087, 3386, 2575, 7625, 1054, 6517, 7878, 190, 6089, 1727, 7678, 28, 6068, 4647, 3803, 1227, 6051, 5673, 3447, 3931, 3680, 4204, 4584, 5086, 5221, 3048, 1216, 7235, 7395, 1898, 1011, 877, 6410, 2418, 3798, 3335, 7371, 3809, 2024, 7764, 7720, 7938, 1247, 2753, 2035, 988, 2423, 7102, 4386, 1312, 6281, 7833, 6802, 2720, 6601, 4487, 3922, 6292, 7501, 2850, 6763, 5230, 4827, 6644, 4820, 1357, 4448, 3129, 2705, 7154, 6967, 5608, 4957, 3144, 1570, 4337, 2639, 4467, 6415, 757, 6612, 6905, 3319, 4094, 7729, 3597, 2539, 5447, 2409, 7959, 3305, 526, 6138, 1839, 7120, 6699, 5990, 3488, 6098, 1187, 7973, 4653, 2434, 5470, 7711, 627, 261, 1258, 6846, 2060, 882, 109, 4798, 2203, 1983, 4141, 3634, 711, 2253, 497, 4595, 5182, 7134, 4162, 7809, 5801, 3846, 5310, 3481, 7169, 2007, 4055, 8144, 5238, 1599, 3972, 3251, 5550, 6716, 2132, 1847, 6840, 2029, 4722, 2166, 3458, 2902, 4765, 2825, 4938, 6178, 952, 4929, 1629, 1906, 3195, 344, 4011, 1669, 4604, 4701, 7660, 5046, 7689, 329, 6074, 3619, 1527, 7800, 7457, 3260, 3277, 1853, 5292, 3814, 611, 7644, 6454, 303, 2498, 2670, 559, 415, 1033, 1382, 7921, 5940, 1391, 5775, 7991, 6651, 444, 7704, 3991, 2313, 4523, 6782, 1471, 4019, 4412, 5851, 155, 5526, 5809, 4182, 3097, 7376, 4229, 540, 384, 4977, 5632, 2951, 4546, 5860, 5018, 5720, 7999, 6392, 2090, 7020, 6982, 690, 3563, 460, 5317, 5259, 7341, 7889, 34, 6152, 8078, 451, 5729, 8024, 6921, 2138, 2586, 3340, 5751, 6990, 4684, 4853, 7253, 5888, 7543, 7439, 943, 6570, 89, 1420, 7861, 6372, 216, 4404, 6692, 3556, 6945, 6473, 2453, 641, 3154, 3825, 294, 5832, 2514, 4118, 3271, 6915, 2747, 1252, 7286, 4299, 2870, 6215, 794, 1684, 5156, 1338, 6831, 6036, 314, 1367, 55, 1552, 1102, 2305, 6900, 2198, 5668, 1307, 379, 4679, 3453, 6449, 8135, 3889, 2865, 73, 2876, 2908, 6438, 7943, 6302, 426, 78, 275, 2115, 5488, 4288, 4263, 4514, 2388, 2372, 1113, 906, 3775, 5205, 6974, 254, 8017, 1501, 3952, 2555, 1710, 5057, 3498, 7367, 6798, 1050, 3676, 7969, 3630, 2701, 7725, 325, 2666, 8140, 2821, 7885, 5884, 6778, 2947, 4675, 5484, 637, 1680, 3534, 5392, 1706, 5880, 3161, 3406, 1606, 2280, 5972, 3538, 5679, 233, 5711, 4026, 3515, 5064, 6221, 3464, 1772, 7769, 1917, 2213, 3894, 5576, 5359, 5396, 2989, 8043, 100, 7521, 5007, 4367, 7058, 1802, 4842, 2490, 3590, 4539, 3086, 2927, 3058, 1610, 6771, 6860, 3296, 5915, 4044, 7592, 3613, 6146, 2018, 2428, 4876, 1129, 6443, 227, 7413, 2284, 4918, 8109, 7145, 1322, 7091, 7403, 1653, 2237, 1205, 1661, 6320, 3210, 6506, 2480, 3751, 3165, 6057, 4882, 2630, 3867, 4326, 6496, 7292, 2172, 6956, 993, 1157, 1272, 7948, 3857, 7066, 3410, 4787, 132, 19, 5167, 973, 6890, 3078, 359, 7602, 7161, 6756, 5768, 2686, 63, 6727, 5683, 3768, 352, 7869, 7042, 7561, 5146, 7817, 2074, 1737, 2040, 2344, 3722, 2881, 6362, 6524, 237, 6867, 860, 3039, 6189, 5783, 896, 5907, 5129, 914, 3243, 3832, 7786, 5245, 2937, 2525, 5976, 1233, 1135, 4377, 1478, 1074, 3505, 4305, 4728, 7211, 2758, 3229, 7028, 2913, 3396, 4249, 3542, 3662, 5378, 6344, 285, 8186, 7192, 6684, 812, 1512, 5617, 820, 4155, 7467, 6662, 6677, 3519, 7854, 7051, 5951, 6464, 481, 741, 5176, 7915, 3023, 6286, 5001, 967, 83, 2366, 4496, 5068, 8180, 6250, 1966, 1093, 6198, 663, 4110, 733, 2324, 7670, 3917, 2404, 5456, 5216, 1377, 5715, 4590, 4924, 2383, 5479, 6565, 6031, 5162, 6184, 7516, 1317, 5345, 1487, 280, 1088, 1639, 4030, 6742, 3648, 1430, 5350, 6256, 6115, 4280, 6734, 5095, 2712, 4577, 6171, 4988, 7179, 6243, 1776, 1331, 8102, 5192, 5871, 5698, 2267, 5655, 3876, 781, 4391, 4905, 1789, 6307, 6483, 1061, 7773, 3065, 847, 7482, 1492, 3431, 5924, 1544, 725, 5560, 7387, 2460, 1822, 8151, 199, 7318, 6225, 4210, 8115, 1885, 6789, 177, 2562, 1344, 4944, 4128, 7107, 7530, 7007, 431, 5513, 5537, 3468, 3182, 402, 2809, 6747, 4502, 3962, 3526, 1536, 1760, 518, 7931, 7450, 367, 1997, 6558, 3898, 2858, 4319, 4355, 5137, 4864, 4001, 2160, 534, 6045, 6606, 1123, 3716, 4293, 2660, 3710, 5580, 961, 1783, 6579, 3653, 575, 7243, 8035, 394, 4623, 2245, 506, 3000, 3698, 680, 5108, 1921, 3686, 7419, 6019, 5120, 3905, 3981, 800, 2831, 8168, 2725, 835, 4742, 4268, 5841, 1810, 2217, 165, 3351, 6269, 1644, 5074, 6634, 1042, 5690, 4635, 3136, 6403, 4694, 3117, 1560, 2397, 2993, 2191, 3203, 6380, 123, 5739, 701, 4170, 2772, 1459, 6807, 1587, 5586, 2120, 6128, 7632, 8047, 1617, 4421, 5420, 4035, 1399, 7225, 8009, 6163, 3783, 4812, 648, 8087, 4062, 6591, 7577, 5363, 3937, 2290, 587, 4530, 5027, 1717, 1690, 4771, 1443, 7838, 6541, 2098, 5493, 4077, 7745, 5400, 5270, 5327, 11, 6261, 6204, 1025, 488, 2800, 932, 6334, 7475, 5413, 4668, 3032, 5440, 5011, 6427, 2356, 1521, 8072, 7758, 5464, 2893, 2651, 5961, 7506, 6013, 581, 2377, 1879, 2624, 4371, 8129, 5705, 6354, 6120, 6879, 4969, 5283, 8159, 2333, 7308, 4224, 5746, 4717, 606, 752, 104, 1222, 7097, 2339, 3224, 4871, 1152, 320, 1912, 7281, 6297, 1582, 6536, 1118, 830, 4900, 7525, 4996, 5340, 7203, 1435, 669, 2578, 7332, 7568, 6008, 1577, 5506, 4070, 5569, 3389, 1976, 4846, 1749, 6624, 1183, 4137, 3125, 4090, 3331, 7829, 7621, 3927, 7337, 7249, 4519, 5628, 7685, 2494, 4051, 4761, 5968, 5355, 2551, 7881, 375, 2111, 2449, 790, 2521, 4245, 6723, 6520, 3747, 7062, 3054, 7409, 7314, 5533, 6239, 1057, 1373, 1635, 6673, 4492, 7573, 7741, 2393, 7628, 5104, 1806, 6554, 3706, 3743, 5100, 1972, 7681, 748, 4896, 5436, 2620, 774, 1452, 2694, 1730, 4460, 3090, 4456, 2470, 5040, 5253, 3792, 6092, 7492, 6106, 7614, 4832, 674, 6585, 5210, 193, 2474, 2931, 1301, 2274, 985, 2717, 1895, 3806, 4644, 4201, 600, 6514, 2057, 708, 1836, 4650, 4464, 3594, 5227, 7151, 5289, 556, 4008, 6071, 6837, 4935, 5798, 5235, 2583, 7540, 6979, 31, 3094, 4543, 7988, 1468, 6435, 4285, 1099, 3450, 2744, 5153, 213, 3151, 1769, 2986, 1703, 5676, 2698, 6775, 5202, 5054, 6953, 4784, 1202, 6054, 2015, 4915, 4839, 6768, 7208, 3659, 911, 1230, 1734, 6864, 7599, 3765, 7513, 6739, 2321, 4587, 3020, 8177, 1509, 7851, 4125, 3179, 5557, 4207, 778, 3062, 5092, 1328, 8165, 162, 4620, 3683, 6042, 958, 1757, 2855, 1440, 5267, 3780, 3934, 1456, 1614, 4632, 2188, 7278, 4993, 2330, 1219, 5958, 8126, 929, 6424, 6670, 6551, 2446, 3051, 7618, 4048, 6005, 1746, 5795, 7985, 597, 5224, 7611, 1298, 5433, 4453, 1754, 4629, 1506, 5089, 4836, 7596, 210, 5199, 1412, 7184, 923, 1014, 5430, 207, 926, 6002, 5935, 6387, 7129, 1901, 7496, 3300, 1017, 1211, 6885, 891, 4362, 7398, 1108, 1675, 1415, 1362, 6629, 7220, 3957, 7238, 6110, 5919, 7187, 658, 3445, 4582, 7676, 3801, 2573, 7876, 1020, 4964, 6279, 6599, 1245, 2421, 3796, 2022, 1214, 1009, 3317, 2537, 1568, 6413, 4446, 6965, 7499, 4825, 1981, 2251, 259, 880, 6096, 2432, 3303, 7118, 2900, 6176, 6714, 2027, 2005, 1597, 7132, 3844, 301, 413, 3258, 3812, 5044, 3617, 1904, 1667, 4975, 5858, 5524, 7374, 2311, 4017, 5938, 6649, 4851, 7437, 8022, 3338, 5257, 6150, 6390, 688, 6213, 1336, 4116, 1250, 6471, 3823, 1418, 4402, 273, 4261, 71, 7941, 1305, 6447, 1365, 2303, 2819, 2945, 3674, 7723, 3950, 3496, 1111, 6972, 5574, 8041, 5062, 7767, 2278, 231, 1678, 5878, 225, 8107, 7590, 2426, 2925, 6858, 4365, 2488, 3855, 130, 6494, 991, 2478, 4880, 7401, 1659, 6360, 858, 5144, 2038, 61, 350, 6888, 7159, 3394, 5376, 3503, 2756, 2935, 1133, 894, 3241, 2364, 6248, 739, 6284, 6660, 7049, 7190, 5615, 1086, 3646, 6029, 1315, 5214, 4922, 661, 7668, 6481, 845, 2265, 4389, 7177, 8100, 6113, 2710, 5511, 400, 2560, 7105, 197, 8113, 5922, 7385, 2658, 1781, 3999, 6604, 1995, 4317, 3960, 516, 5839, 3349, 3979, 2723, 678, 7417, 7241, 2243, 6126, 4419, 699, 6805, 1558, 3201, 6632, 3134, 4075, 5325, 1715, 7836, 6589, 2288, 7223, 4810, 1877, 5703, 5462, 7504, 3030, 2354, 1023, 6332, 828, 5338, 1150, 6295, 604, 7095, 4967, 7306, 5626, 4759, 4088, 3925, 3387, 6622, 2576, 1575, 7626, 3704, 1055, 4490, 6518, 7407, 7879, 788, 191, 2272, 6090, 4830, 1728, 2468, 7679, 2618, 29, 1466, 6069, 5233, 4648, 7149, 3804, 6512, 1228, 3763, 6052, 6766, 5674, 5052, 3448, 3149, 3932, 2186, 3681, 2853, 4205, 1326, 4585, 7849, 5087, 5197, 5222, 4451, 3049, 1744, 1217, 6422, 7236, 656, 7396, 1360, 1899, 1209, 1012, 6000, 878, 7116, 6411, 4823, 2419, 1007, 3799, 4962, 3336, 686, 7372, 6647, 3810, 1665, 2025, 3842, 7765, 5876, 7721, 6970, 7939, 2301, 1248, 4400, 2754, 3239, 2036, 7157, 989, 1657, 2424, 2486, 7103, 7383, 4387, 2708, 1313, 7666, 6282, 5613, 7834, 4808, 6803, 3132, 2721, 2241, 6602, 514, 4488, 786, 3923, 1573, 6293, 7304, 7502, 6330, 2851, 7847, 6764, 3147, 5231, 6510, 4828, 2616, 6645, 3840, 4821, 4960, 1358, 5998, 4449, 6420, 3130, 512, 2706, 5611, 7155, 2484, 6968, 4398, 5609, 4396, 4958, 6418, 3145, 2614, 1571, 6328, 4338, 6814, 2640, 4470, 4468, 6324, 6416, 6326, 758, 1167, 6613, 2642, 6906, 4707, 3320, 4472, 4095, 4562, 7730, 4340, 3598, 3214, 2540, 6816, 5448, 5660, 2410, 3322, 7960, 2047, 3306, 4474, 527, 7908, 6139, 6908, 1840, 6061, 7121, 4709, 6700, 4432, 5991, 6615, 3489, 1291, 6099, 2644, 1188, 3006, 7974, 760, 4654, 4886, 2435, 1169, 5471, 3881, 7712, 2542, 628, 2734, 262, 6818, 1259, 7078, 6847, 3600, 2061, 3755, 883, 3216, 110, 3104, 4799, 7732, 2204, 4610, 1984, 4342, 4142, 468, 3635, 4097, 712, 3169, 2254, 4564, 498, 6312, 4596, 3308, 5183, 5599, 7135, 4476, 4163, 5648, 7810, 7962, 5802, 4330, 3847, 2049, 5311, 7654, 3482, 2412, 7170, 4439, 2008, 3324, 4056, 3692, 8145, 5450, 5239, 6500, 1600, 5662, 3973, 6488, 3252, 7123, 5551, 1830, 6717, 4711, 2133, 4177, 1848, 1842, 6841, 2634, 2030, 6063, 4723, 2069, 2167, 6141, 3459, 3625, 2903, 6910, 4766, 2767, 2826, 529, 4939, 3871, 6179, 7910, 953, 4910, 4930, 6101, 1630, 7824, 1907, 2646, 3196, 8095, 345, 3491, 4012, 6960, 1670, 1293, 4605, 1286, 4702, 5993, 7661, 1002, 5047, 6617, 7690, 7425, 330, 6702, 6075, 997, 3620, 4434, 1528, 1794, 7801, 2437, 7458, 3377, 3261, 1171, 3278, 8060, 1854, 4656, 5293, 7296, 3815, 4888, 612, 4189, 7645, 7976, 6455, 6080, 304, 762, 2499, 2974, 2671, 1190, 560, 2176, 416, 3008, 1034, 3070, 1383, 264, 7922, 5301, 5941, 6820, 1392, 3424, 5776, 630, 7992, 7952, 6652, 2736, 445, 7794, 7705, 7714, 3992, 6707, 2314, 2544, 4524, 5114, 6783, 5473, 1472, 3861, 4020, 3883, 4413, 852, 5852, 885, 156, 550, 5527, 3218, 5810, 2779, 4183, 2063, 3098, 1161, 7377, 3757, 4230, 2785, 541, 6849, 385, 335, 4978, 3602, 5633, 3362, 2952, 1261, 4547, 1276, 5861, 7080, 5019, 1066, 5721, 1986, 8000, 2081, 6393, 4344, 2091, 7000, 7021, 2206, 6983, 4791, 691, 4612, 3564, 2967, 461, 4801, 5318, 7430, 5260, 7734, 7342, 1927, 7890, 112, 35, 136, 6153, 3106, 8079, 7778, 452, 2256, 5730, 146, 8025, 4566, 6922, 2595, 2139, 714, 2587, 7070, 3341, 3171, 5752, 5816, 6991, 3637, 4685, 7695, 4854, 4099, 7254, 3571, 5889, 4144, 7544, 3414, 7440, 470, 944, 3436, 6571, 7137, 90, 1865, 1421, 4478, 7862, 7360, 6373, 5185, 217, 977, 4405, 5601, 6693, 871, 3557, 4598, 6946, 1176, 6474, 3310, 2454, 3911, 642, 500, 3155, 6894, 3826, 6314, 295, 5929, 5833, 3849, 2515, 4218, 4119, 2051, 3272, 2127, 6916, 5804, 2748, 23, 1253, 4332, 7287, 3608, 4300, 7812, 2871, 3266, 6216, 7964, 795, 2155, 1685, 4165, 5157, 5171, 1339, 5650, 6832, 7487, 6037, 2010, 315, 2888, 1368, 3326, 56, 3945, 1553, 7172, 1103, 7606, 2306, 4441, 6901, 1353, 2199, 3484, 5669, 3382, 1308, 2414, 380, 3987, 4680, 5313, 3454, 7165, 6450, 7656, 8136, 1497, 3890, 1602, 2866, 6941, 74, 5664, 2877, 2682, 2909, 5241, 6439, 3082, 7944, 6502, 6303, 4984, 427, 8147, 79, 7463, 276, 5452, 2116, 3113, 5489, 4058, 4289, 363, 4264, 3694, 4515, 5565, 2389, 6719, 2373, 4664, 1114, 4713, 907, 1699, 3776, 5553, 5206, 2690, 6975, 1832, 255, 1241, 8018, 3254, 1502, 2442, 3953, 7125, 2556, 6025, 1711, 3975, 5058, 67, 3499, 6490, 7368, 7392, 6799, 2032, 1051, 1146, 3677, 6065, 7970, 6135, 3631, 6843, 2702, 6760, 7726, 2636, 326, 341, 2667, 1850, 8141, 7806, 2822, 1844, 7886, 7017, 5885, 2135, 6779, 5772, 2948, 4179, 4676, 1549, 5485, 2905, 638, 6369, 1681, 6912, 3535, 5389, 5393, 3461, 1707, 3772, 5881, 3627, 3162, 2234, 3407, 2169, 1607, 1799, 2281, 6143, 5973, 5126, 3539, 4725, 5680, 356, 234, 2071, 5712, 730, 4027, 6181, 3516, 809, 5065, 7912, 6222, 722, 3465, 4941, 1773, 6731, 7770, 3873, 1918, 391, 2214, 2828, 3895, 1533, 5577, 531, 5360, 6160, 5397, 4768, 2990, 5687, 8044, 2769, 101, 8156, 7522, 1909, 5008, 2797, 4368, 2648, 7059, 2108, 1803, 1632, 4843, 7565, 2491, 7826, 3591, 4198, 4540, 4932, 3087, 4893, 2928, 6103, 3059, 8174, 1611, 955, 6772, 5150, 6861, 4912, 3297, 204, 5916, 1672, 4045, 8123, 7593, 1295, 3614, 1594, 6147, 4014, 2019, 7873, 2429, 6962, 4877, 6855, 1130, 347, 6444, 3820, 228, 3493, 7414, 4314, 2285, 3198, 4919, 7046, 8110, 8097, 7146, 2465, 1323, 5049, 7092, 2351, 7404, 6619, 1654, 2298, 2238, 7663, 1206, 1741, 1662, 1004, 6321, 2611, 3211, 4704, 6507, 7301, 2481, 5995, 3752, 2731, 3166, 4607, 6058, 2044, 4883, 1288, 2631, 1827, 3868, 3622, 4327, 5596, 6497, 4436, 7293, 3374, 2173, 6077, 6957, 7821, 994, 999, 1158, 547, 1273, 332, 7949, 5298, 3858, 6704, 7067, 143, 3411, 7692, 4788, 2078, 133, 7427, 20, 4215, 5168, 3263, 974, 1862, 6891, 1173, 3079, 6938, 360, 7460, 7603, 2885, 7162, 3379, 6757, 1143, 5769, 7803, 2687, 4661, 64, 2439, 6728, 806, 5684, 1530, 3769, 6366, 353, 1796, 7870, 8120, 7043, 3817, 7562, 2794, 5147, 4890, 7818, 5593, 2075, 5295, 1738, 2348, 2041, 7298, 2345, 2791, 3723, 1856, 2882, 1859, 6363, 4658, 6525, 1950, 238, 3280, 6868, 3726, 861, 8062, 3040, 7323, 6190, 306, 5784, 3729, 897, 764, 5908, 5825, 5130, 6457, 915, 6871, 3244, 6082, 3833, 4752, 7787, 7647, 5246, 8065, 2938, 7978, 2526, 2837, 5977, 614, 1234, 864, 1136, 4191, 4378, 6230, 1479, 418, 1075, 1953, 3506, 3010, 4306, 2147, 4729, 562, 7212, 6528, 2759, 2178, 3230, 4236, 7029, 2673, 2914, 3283, 3397, 1192, 4250, 42, 3543, 2501, 3663, 241, 5379, 2976, 6345, 182, 286, 5943, 8187, 3732, 7193, 6822, 6685, 3583, 813, 7924, 1513, 5787, 5618, 5303, 821, 2844, 4156, 1385, 7468, 767, 6663, 266, 6678, 4274, 3520, 1036, 7855, 900, 7052, 3072, 5952, 2567, 6465, 6654, 482, 7326, 742, 2738, 5177, 1624, 7916, 7994, 3024, 3043, 6287, 7954, 5002, 7086, 968, 5778, 84, 309, 2367, 632, 4497, 570, 5069, 1394, 8181, 6193, 6251, 3426, 1967, 1890, 1094, 2316, 6199, 6874, 664, 2546, 4111, 7585, 734, 3994, 2325, 918, 7671, 6709, 3918, 4953, 2405, 7707, 5457, 6085, 5217, 7716, 1378, 5847, 5716, 447, 4591, 3247, 4925, 7796, 2384, 6794, 5480, 4022, 6566, 5828, 6032, 3885, 5163, 7038, 6185, 1474, 7517, 5911, 1318, 3863, 5346, 5867, 1488, 6785, 281, 6460, 1089, 5475, 1640, 119, 4031, 4526, 6743, 5133, 3649, 5116, 1431, 4133, 5351, 5529, 6257, 8068, 6116, 3220, 4281, 4780, 6735, 158, 5096, 5249, 2713, 552, 4578, 2533, 6172, 5854, 4989, 7981, 7180, 887, 6244, 841, 1777, 4415, 1332, 2941, 8103, 854, 5193, 7112, 5872, 7379, 5699, 4755, 2268, 3759, 5656, 4428, 3877, 3100, 782, 3836, 4392, 1163, 4906, 1282, 1790, 4185, 6308, 7650, 6484, 2065, 1062, 2963, 7774, 5812, 3066, 7790, 848, 2781, 7483, 1349, 1493, 4980, 3432, 867, 5925, 3604, 1545, 2230, 726, 387, 5561, 1237, 7388, 337, 2461, 2607, 1823, 543, 8152, 4194, 200, 6851, 7319, 4748, 6226, 4232, 4211, 1139, 8116, 2787, 1886, 4949, 6790, 5863, 178, 2840, 2563, 7082, 1345, 2603, 4945, 4549, 4129, 2529, 7108, 1278, 7531, 4553, 7008, 2954, 432, 617, 5514, 1263, 5538, 7897, 3469, 5635, 3183, 5980, 403, 3364, 2810, 436, 6748, 6395, 4503, 1956, 3963, 4346, 3527, 5900, 1537, 8002, 1761, 1078, 519, 2083, 7932, 621, 7451, 5723, 368, 3013, 1998, 1988, 6559, 171, 3899, 5021, 2859, 3509, 4320, 1068, 4356, 5518, 5138, 693, 4865, 6233, 4002, 4614, 2161, 7639, 535, 6985, 6046, 4381, 6607, 4793, 1124, 1267, 3717, 7023, 4294, 421, 2661, 2208, 3711, 4737, 5581, 2093, 962, 1482, 1784, 7002, 6580, 7535, 3654, 5262, 576, 6531, 7244, 7736, 8036, 5371, 395, 5320, 4624, 7215, 2246, 7432, 507, 4557, 3001, 463, 3699, 2181, 681, 4803, 5109, 3357, 1922, 3566, 3687, 2762, 7420, 2969, 6020, 7012, 5121, 6155, 3906, 2150, 3982, 3108, 801, 1945, 2832, 37, 8169, 4309, 2726, 138, 836, 2958, 4743, 7892, 4269, 565, 5842, 114, 1811, 1934, 2218, 7344, 166, 4732, 3352, 1929, 6270, 3187, 1645, 8027, 5075, 3286, 6635, 4568, 1043, 7554, 5691, 5732, 4636, 2917, 3137, 148, 6404, 5984, 4695, 454, 3118, 1195, 1561, 2258, 2398, 1816, 2994, 8081, 2192, 3400, 3204, 7780, 6381, 407, 124, 3343, 5740, 4239, 702, 3173, 4171, 8054, 2773, 2589, 1460, 3233, 6808, 7072, 1588, 3368, 5587, 2141, 2121, 2676, 6129, 716, 7633, 1939, 8048, 6924, 1618, 7032, 4422, 2597, 5421, 5542, 4036, 4856, 1400, 244, 7226, 4101, 8010, 5761, 6164, 4687, 3784, 3666, 4813, 7697, 649, 7901, 8088, 6993, 4063, 2979, 6592, 3639, 7578, 2223, 5364, 5754, 3938, 5382, 2291, 5818, 588, 3473, 4531, 7442, 5028, 45, 1718, 472, 1691, 6930, 4772, 7546, 1444, 4253, 7839, 3416, 6542, 5639, 2099, 5891, 5494, 2504, 4078, 4146, 7746, 7349, 5401, 7256, 5271, 3546, 5328, 3573, 12, 4507, 6262, 1423, 6205, 3735, 1026, 4480, 489, 7269, 2801, 92, 933, 8190, 6335, 1867, 7476, 1960, 5414, 6573, 4669, 6825, 3033, 7139, 5441, 5080, 5012, 946, 6428, 7196, 2357, 3438, 1522, 3967, 8073, 4407, 7759, 185, 5465, 5603, 2894, 1406, 2652, 219, 5962, 6348, 7507, 979, 6014, 4350, 582, 6375, 2378, 5946, 1880, 5187, 2625, 3291, 4372, 7864, 8130, 289, 5706, 7362, 6355, 2814, 6121, 6476, 6880, 5790, 4970, 3312, 5284, 5035, 8160, 6948, 2334, 1516, 7309, 1178, 4225, 440, 5747, 3559, 4718, 5306, 607, 4600, 753, 6640, 105, 6695, 1223, 5621, 7098, 873, 2340, 6752, 3225, 3828, 4872, 3586, 1153, 6316, 321, 250, 1913, 3157, 7282, 6688, 6298, 6896, 1583, 6399, 6537, 644, 1119, 7927, 831, 502, 4901, 4573, 7526, 2456, 4997, 816, 5341, 3913, 7204, 1765, 1436, 4121, 670, 770, 2579, 2053, 7333, 5502, 7569, 2517, 6009, 7471, 1578, 4220, 5507, 1082, 4071, 5835, 5570, 269, 3390, 3851, 1977, 6275, 4847, 297, 1750, 6666, 6625, 5931, 1184, 523, 4138, 1255, 3126, 2847, 4091, 4334, 3332, 7232, 7830, 2750, 7622, 824, 3928, 25, 7338, 2087, 7250, 6918, 4520, 1388, 5629, 5806, 7686, 3192, 2495, 3274, 4052, 4159, 4762, 2129, 5969, 3531, 5356, 6218, 2552, 903, 7882, 7966, 376, 52, 2112, 2873, 2450, 7858, 791, 3268, 2522, 5904, 4246, 4302, 6724, 3075, 6521, 7814, 3748, 1650, 7063, 7289, 3055, 7055, 7410, 3610, 7315, 1541, 5534, 1341, 6240, 4277, 1058, 5652, 1374, 4107, 1636, 5159, 6674, 6681, 4493, 5173, 7574, 8006, 7742, 1687, 2394, 1039, 7629, 4167, 5105, 8032, 1807, 797, 6555, 3523, 3707, 2157, 3744, 372, 5101, 1370, 1973, 7329, 7682, 3328, 749, 5280, 4897, 317, 5437, 485, 2621, 2890, 775, 3017, 1453, 6039, 2695, 2741, 1731, 2012, 4461, 4641, 3091, 6834, 4457, 745, 2471, 7489, 5041, 2002, 5254, 2308, 3793, 2570, 6093, 4443, 7493, 5427, 6107, 1105, 7615, 5955, 4833, 7608, 675, 1992, 6586, 1555, 5211, 6657, 194, 7174, 2475, 2922, 2932, 58, 1302, 6468, 2275, 3947, 986, 7936, 2718, 1310, 1896, 3046, 3807, 2416, 4645, 1725, 4202, 5671, 601, 3027, 6515, 3384, 2058, 625, 709, 2201, 1837, 7957, 4651, 3486, 4465, 3142, 3595, 6903, 5228, 6290, 7152, 1355, 5290, 7455, 557, 6452, 4009, 1627, 6072, 7658, 6838, 5548, 4936, 3456, 5799, 5180, 5236, 7167, 2584, 5727, 7541, 4682, 6980, 7997, 32, 5315, 3095, 153, 4544, 382, 7989, 7919, 1469, 3989, 6436, 2863, 4286, 76, 1100, 312, 3451, 5666, 2745, 2512, 5154, 2868, 214, 87, 3152, 6943, 1770, 3513, 2987, 3892, 1704, 635, 5677, 1604, 2699, 1048, 6776, 8138, 5203, 2370, 5055, 1499, 6954, 4324, 4785, 7946, 1203, 7089, 6055, 6504, 2016, 4042, 4916, 6441, 4840, 5005, 6769, 3084, 7209, 1072, 3660, 2911, 912, 5781, 1231, 5243, 1735, 7559, 6865, 2879, 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3264, 3606, 975, 7358, 1863, 3434, 6892, 3909, 1174, 869, 3080, 2680, 6939, 1495, 361, 3111, 7461, 4982, 7604, 3943, 2886, 7485, 7163, 3985, 3380, 1351, 6758, 6133, 1144, 7390, 5770, 7015, 7804, 339, 2688, 1697, 4662, 5563, 65, 6023, 2440, 1239, 6729, 720, 807, 728, 5685, 6158, 1531, 389, 3770, 5387, 6367, 1547, 354, 5124, 1797, 2232, 7871, 1592, 8121, 202, 7044, 4312, 3818, 6853, 7563, 2106, 2795, 8154, 5148, 8172, 4891, 4196, 7819, 3372, 5594, 1825, 2076, 141, 5296, 545, 1739, 2296, 2349, 2463, 2042, 2729, 7299, 2609, 2346, 5591, 2792, 8118, 3724, 1948, 1857, 2789, 2883, 6936, 1860, 4213, 6364, 804, 4659, 1141, 6526, 2145, 1951, 6228, 239, 40, 3281, 4234, 6869, 5823, 3727, 7321, 862, 2835, 8063, 4750, 3041, 1622, 7324, 2565, 6191, 568, 307, 7084, 5785, 3581, 3730, 180, 898, 4272, 765, 2842, 5909, 7036, 5826, 6792, 5131, 117, 6458, 5865, 916, 7583, 6872, 1888, 3245, 5845, 6083, 4951, 3834, 4426, 4753, 7110, 7788, 2961, 7648, 1280, 5247, 4778, 8066, 4131, 2939, 839, 7979, 2531, 2527, 2601, 2838, 4947, 5978, 7895, 615, 4551, 1235, 2228, 865, 1347, 1137, 4746, 4192, 2605, 4379, 7637, 6231, 5516, 1480, 4735, 419, 1265, 1076, 5898, 1954, 434, 3507, 169, 3011, 619, 4307, 1943, 2148, 7010, 4730, 1932, 563, 2956, 7213, 5369, 6529, 7533, 2760, 3355, 2179, 4555, 3231, 8052, 4237, 405, 7030, 1937, 2674, 3366, 2915, 7552, 3284, 3185, 3398, 1814, 1193, 5982, 4251, 6928, 43, 3471, 3544, 7347, 2502, 5637, 3664, 5759, 242, 5540, 5380, 2221, 2977, 7899, 6346, 1404, 183, 3965, 287, 3289, 5944, 4348, 8188, 7267, 3733, 4505, 7194, 5078, 6823, 1958, 6686, 248, 3584, 6750, 814, 4571, 7925, 6397, 1514, 5033, 5788, 2812, 5619, 6638, 5304, 438, 822, 7230, 2845, 521, 4157, 3190, 1386, 2085, 7469, 5500, 768, 1763, 6664, 6273, 267, 1080, 6679, 4105, 4275, 1539, 3521, 8030, 1037, 8004, 7856, 50, 901, 3529, 7053, 1648, 3073, 5902, 5953, 5425, 2568, 2000, 6466, 2920, 6655, 1990, 483, 5278, 7327, 370, 743, 4639, 2739, 3015, 5178, 5546, 1625, 7453, 7917, 151, 7995, 5725, 3025, 1723, 3044, 7934, 6288, 3140, 7955, 623, 5003, 4040, 7087, 4322, 969, 7557, 5779, 1070, 85, 2510, 310, 2861, 2368, 1046, 633, 3511, 4498, 4860, 571, 3901, 5070, 5735, 1395, 5023, 8182, 477, 6194, 6561, 6252, 5694, 3427, 173, 1968, 3788, 1891, 4004, 1095, 1198, 2317, 4616, 6200, 7754, 6875, 4867, 665, 3121, 2547, 6235, 4112, 3670, 7586, 5140, 735, 2261, 3995, 695, 2326, 593, 919, 4358, 7672, 1564, 6710, 5520, 3919, 4817, 4954, 6609, 2406, 5987, 7708, 4795, 5458, 4084, 6086, 6048, 5218, 6407, 7717, 4383, 1379, 7701, 5848, 537, 5717, 457, 448, 6987, 4592, 3478, 3248, 2163, 4926, 4698, 7797, 7641, 2385, 8014, 6795, 2663, 5481, 3403, 4023, 2210, 6567, 3553, 5829, 4296, 6033, 2195, 3886, 423, 5164, 5765, 7039, 3719, 6186, 7783, 1475, 7025, 7518, 4536, 5912, 1126, 1319, 3207, 3864, 1269, 5347, 6168, 5868, 1786, 1489, 1819, 6786, 7004, 282, 4152, 6461, 964, 1090, 2401, 5476, 1484, 1641, 4691, 120, 5583, 4032, 8084, 4527, 2095, 6744, 7447, 5134, 3713, 3650, 2997, 5117, 4739, 1432, 4067, 4134, 7246, 5352, 4242, 5530, 7738, 6258, 5410, 8069, 578, 6117, 5743, 3221, 6533, 4282, 2983, 4781, 3656, 6736, 3176, 159, 5264, 5097, 1449, 5250, 6582, 2714, 705, 553, 7537, 4579, 6596, 2534, 2248, 6173, 410, 5855, 7434, 4990, 6548, 7982, 4626, 7181, 6384, 888, 7217, 6245, 3643, 842, 397, 1778, 3346, 4416, 5322, 1333, 4258, 2942, 8038, 8104, 127, 855, 5373, 5194, 653, 7113, 683, 5873, 3236, 7380, 4805, 5700, 5335, 4756, 3701, 2269, 1463, 3760, 2183, 5657, 7905, 4429, 3003, 3878, 7075, 3101, 465, 783, 7844, 3837, 509, 4393, 6811, 1164, 4559, 4907, 8092, 1283, 7422, 1791, 8057, 4186, 2971, 6309, 5645, 7651, 3689, 6485, 4174, 2066, 2764, 1063, 6997, 2964, 1924, 7775, 2592, 5813, 3568, 3067, 3421, 7791, 5111, 849, 2776, 2782, 3359, 7484, 3942, 1350, 3984, 1494, 2679, 4981, 3110, 3433, 7357, 868, 3908, 5926, 2124, 3605, 2152, 1546, 5386, 2231, 5123, 727, 719, 388, 6157, 5562, 1696, 1238, 6022, 7389, 6132, 338, 7014, 2462, 2295, 2608, 2728, 1824, 3371, 544, 140, 8153, 2105, 4195, 8171, 201, 1591, 6852, 4311, 7320, 5822, 4749, 2834, 6227, 2144, 4233, 39, 4212, 6935, 1140, 803, 8117, 5590, 2788, 1947, 1887, 7582, 4950, 5844, 6791, 7035, 5864, 116, 179, 3580, 2841, 4271, 2564, 1621, 7083, 567, 1346, 2227, 2604, 4745, 4946, 2600, 4550, 7894, 4130, 4777, 2530, 838, 7109, 4425, 1279, 2960, 7532, 5368, 4554, 3354, 7009, 1942, 2955, 1931, 433, 5897, 618, 168, 5515, 7636, 1264, 4734, 5539, 5758, 7898, 2220, 3470, 6927, 5636, 7346, 3184, 7551, 5981, 1813, 404, 8051, 3365, 1936, 2811, 5032, 437, 6637, 6749, 247, 6396, 4570, 4504, 7266, 1957, 5077, 3964, 1403, 4347, 3288, 3528, 49, 5901, 1647, 1538, 4104, 8003, 8029, 1762, 5499, 1079, 6272, 520, 7229, 2084, 3189, 7933, 1722, 622, 3139, 7452, 5545, 5724, 150, 369, 5277, 3014, 4638, 1999, 5424, 1989, 2919, 6560, 476, 172, 5693, 3900, 4859, 5022, 5734, 2860, 2509, 3510, 1045, 4321, 4039, 1069, 7556, 4357, 592, 5519, 1563, 5139, 3669, 694, 2260, 4866, 7753, 6234, 3120, 4003, 3787, 4615, 1197, 2162, 3477, 7640, 4697, 536, 7700, 6986, 456, 6047, 4083, 4382, 6406, 6608, 4816, 4794, 5986, 1125, 4535, 1268, 3206, 3718, 5764, 7024, 7782, 4295, 3552, 422, 2194, 2662, 8013, 2209, 3402, 3712, 7446, 4738, 2996, 5582, 4690, 2094, 8083, 963, 4151, 1483, 2400, 1785, 6167, 7003, 1818, 6581, 1448, 7536, 704, 3655, 2982, 5263, 3175, 577, 5409, 6532, 5742, 7245, 4066, 7737, 4241, 8037, 4257, 5372, 126, 396, 3642, 5321, 3345, 4625, 6547, 7216, 6383, 2247, 6595, 7433, 409, 508, 7843, 4558, 6810, 3002, 7904, 464, 7074, 3700, 5334, 2182, 1462, 682, 652, 4804, 3235, 5110, 3420, 3358, 2775, 1923, 6996, 3567, 2591, 3688, 5644, 2763, 4173, 7421, 8091, 2970, 8056, 6021, 1695, 7013, 6131, 5122, 5385, 6156, 718, 3907, 7356, 2151, 2123, 3983, 3941, 3109, 2678, 802, 6934, 1946, 5589, 2833, 5821, 38, 2143, 8170, 2104, 4310, 1590, 2727, 2294, 139, 3370, 837, 4776, 2959, 4424, 4744, 2226, 7893, 2599, 4270, 3579, 566, 1620, 5843, 7581, 115, 7034, 1812, 7550, 1935, 8050, 2219, 5757, 7345, 6926, 167, 5896, 4733, 7635, 3353, 5367, 1930, 1941, 6271, 5498, 3188, 7228, 1646, 48, 8028, 4103, 5076, 7265, 3287, 1402, 6636, 5031, 4569, 246, 1044, 2508, 7555, 4038, 5692, 475, 5733, 4858, 4637, 5276, 2918, 5423, 3138, 1721, 149, 5544, 6405, 4082, 5985, 4815, 4696, 3476, 455, 7699, 3119, 7752, 1196, 3786, 1562, 591, 2259, 3668, 2399, 4150, 1817, 6166, 2995, 7445, 8082, 4689, 2193, 3551, 3401, 8012, 3205, 4534, 7781, 5763, 6382, 6546, 408, 6594, 125, 4256, 3344, 3641, 5741, 5408, 4240, 4065, 703, 1447, 3174, 2981, 4172, 5643, 8055, 8090, 2774, 3419, 2590, 6995, 1461, 5333, 3234, 651, 6809, 7842, 7073, 7903, 1589, 2103, 3369, 2293, 5588, 6933, 2142, 5820, 2122, 7355, 2677, 3940, 6130, 1694, 717, 5384, 7634, 5895, 1940, 5366, 8049, 7549, 6925, 5756, 1619, 3578, 7033, 7580, 4423, 4775, 2598, 2225, 5422, 5275, 5543, 1720, 4037, 2507, 4857, 474, 1401, 7264, 245, 5030, 7227, 5497, 4102, 47, 8011, 3550, 5762, 4533, 6165, 4149, 4688, 7444, 3785, 7751, 3667, 590, 4814, 4081, 7698, 3475, 650, 5332, 7902, 7841, 8089, 5642, 6994, 3418, 4064, 5407, 2980, 1446, 6593, 6545, 3640, 4255, 7579, 3577, 2224, 4774, 5365, 5894, 5755, 7548, 3939, 7354, 5383, 1693, 2292, 2102, 5819, 6932, 589, 7750, 3474, 4080, 4532, 3549, 7443, 4148, 5029, 7263, 46, 5496, 1719, 5274, 473, 2506, 1692, 7353, 6931, 2101, 4773, 3576, 7547, 5893, 1445, 5406, 4254, 6544, 7840, 5331, 3417, 5641, 6543, 5405, 5640, 5330, 2100, 7352, 5892, 3575, 5495, 7262, 2505, 5273, 4079, 7749, 4147, 3548, 7747, 7260, 7350, 5403, 5402, 7259, 7257, 7258, 5272, 7261, 3547, 7748, 5329, 5404, 3574, 7351}; +constexpr uint16_t EXP_TABLE_13[] = {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 27, 54, 108, 216, 432, 864, 1728, 3456, 6912, 5659, 3117, 6234, 4271, 325, 650, 1300, 2600, 5200, 2235, 4470, 759, 1518, 3036, 6072, 3947, 7894, 7607, 7029, 5873, 3577, 7154, 6143, 4069, 8138, 8079, 7941, 7697, 7225, 6249, 4297, 393, 786, 1572, 3144, 6288, 4411, 621, 1242, 2484, 4968, 1739, 3478, 6956, 5699, 3229, 6458, 4719, 1221, 2442, 4884, 1587, 3174, 6348, 4483, 797, 1594, 3188, 6376, 4555, 909, 1818, 3636, 7272, 6347, 4493, 769, 1538, 3076, 6152, 4107, 13, 26, 52, 104, 208, 416, 832, 1664, 3328, 6656, 5147, 2093, 4186, 175, 350, 700, 1400, 2800, 5600, 3035, 6070, 3959, 7918, 7623, 7061, 5937, 3705, 7410, 6655, 5093, 2001, 4002, 8004, 7827, 7485, 6753, 5337, 2473, 4946, 1727, 3454, 6908, 5603, 3037, 6074, 3951, 7902, 7591, 6997, 5809, 3449, 6898, 5631, 3045, 6090, 3983, 7966, 7719, 7253, 6321, 4473, 745, 1490, 2980, 5960, 3723, 7446, 6711, 5237, 2289, 4578, 991, 1982, 3964, 7928, 7659, 7117, 6017, 3865, 7730, 7295, 6373, 4561, 953, 1906, 3812, 7624, 7051, 5901, 3585, 7170, 6175, 4133, 81, 162, 324, 648, 1296, 2592, 5184, 2203, 4406, 631, 1262, 2524, 5048, 1899, 3798, 7596, 6979, 5789, 3361, 6722, 5279, 2341, 4682, 1167, 2334, 4668, 1123, 2246, 4492, 771, 1542, 3084, 6168, 4139, 77, 154, 308, 616, 1232, 2464, 4928, 1691, 3382, 6764, 5315, 2461, 4922, 1647, 3294, 6588, 4963, 1757, 3514, 7028, 5875, 3581, 7162, 6127, 4037, 8074, 7951, 7685, 7185, 6201, 4201, 201, 402, 804, 1608, 3216, 6432, 4699, 1197, 2394, 4788, 1395, 2790, 5580, 2947, 5894, 3607, 7214, 6215, 4245, 305, 610, 1220, 2440, 4880, 1595, 3190, 6380, 4547, 925, 1850, 3700, 7400, 6603, 5005, 1793, 3586, 7172, 6163, 4157, 97, 194, 388, 776, 1552, 3104, 6208, 4251, 301, 602, 1204, 2408, 4816, 1467, 2934, 5868, 3523, 7046, 5911, 3637, 7274, 6351, 4485, 785, 1570, 3140, 6280, 4363, 525, 1050, 2100, 4200, 203, 406, 812, 1624, 3248, 6496, 4827, 1453, 2906, 5812, 3443, 6886, 5591, 2997, 5994, 3791, 7582, 6951, 5717, 3249, 6498, 4831, 1445, 2890, 5780, 3379, 6758, 5335, 2485, 4970, 1743, 3486, 6972, 5731, 3293, 6586, 4975, 1733, 3466, 6932, 5683, 3197, 6394, 4591, 965, 1930, 3860, 7720, 7243, 6285, 4353, 537, 1074, 2148, 4296, 395, 790, 1580, 3160, 6320, 4475, 749, 1498, 2996, 5992, 3787, 7574, 6967, 5749, 3313, 6626, 5087, 1957, 3914, 7828, 7475, 6781, 5345, 2521, 5042, 1919, 3838, 7676, 7139, 6109, 4001, 8002, 7839, 7461, 6737, 5305, 2409, 4818, 1471, 2942, 5884, 3555, 7110, 6039, 3893, 7786, 7375, 6533, 4881, 1593, 3186, 6372, 4563, 957, 1914, 3828, 7656, 7115, 6029, 3841, 7682, 7199, 6181, 4177, 185, 370, 740, 1480, 2960, 5920, 3675, 7350, 6519, 4853, 1521, 3042, 6084, 3987, 7974, 7767, 7349, 6513, 4857, 1513, 3026, 6052, 3923, 7846, 7511, 6837, 5489, 2809, 5618, 3071, 6142, 4071, 8142, 8071, 7957, 7729, 7289, 6377, 4553, 905, 1810, 3620, 7240, 6283, 4365, 513, 1026, 2052, 4104, 11, 22, 44, 88, 176, 352, 704, 1408, 2816, 5632, 3099, 6198, 4215, 245, 490, 980, 1960, 3920, 7840, 7515, 6829, 5441, 2713, 5426, 2687, 5374, 2535, 5070, 1927, 3854, 7708, 7203, 6237, 4257, 345, 690, 1380, 2760, 5520, 2875, 5750, 3319, 6638, 5063, 1941, 3882, 7764, 7347, 6525, 4833, 1497, 2994, 5988, 3795, 7590, 6999, 5813, 3441, 6882, 5599, 2981, 5962, 3727, 7454, 6695, 5205, 2225, 4450, 735, 1470, 2940, 5880, 3563, 7126, 6071, 3957, 7914, 7631, 7045, 5905, 3641, 7282, 6399, 4581, 977, 1954, 3908, 7816, 7435, 6669, 5121, 2073, 4146, 127, 254, 508, 1016, 2032, 4064, 8128, 8091, 7981, 7745, 7321, 6441, 4681, 1161, 2322, 4644, 1107, 2214, 4428, 643, 1286, 2572, 5144, 2091, 4182, 183, 366, 732, 1464, 2928, 5856, 3547, 7094, 6007, 3829, 7658, 7119, 6021, 3857, 7714, 7263, 6309, 4433, 697, 1394, 2788, 5576, 2955, 5910, 3639, 7278, 6343, 4501, 817, 1634, 3268, 6536, 4875, 1549, 3098, 6196, 4211, 253, 506, 1012, 2024, 4048, 8096, 8027, 7853, 7489, 6809, 5417, 2633, 5266, 2367, 4734, 1255, 2510, 5020, 1827, 3654, 7308, 6403, 4637, 1057, 2114, 4228, 275, 550, 1100, 2200, 4400, 635, 1270, 2540, 5080, 1963, 3926, 7852, 7491, 6813, 5409, 2649, 5298, 2431, 4862, 1511, 3022, 6044, 3875, 7750, 7319, 6453, 4721, 1273, 2546, 5092, 2003, 4006, 8012, 7811, 7453, 6689, 5209, 2217, 4434, 703, 1406, 2812, 5624, 3051, 6102, 4023, 8046, 7879, 7573, 6961, 5753, 3305, 6610, 5055, 1893, 3786, 7572, 6963, 5757, 3297, 6594, 5023, 1829, 3658, 7316, 6451, 4733, 1249, 2498, 4996, 1811, 3622, 7244, 6275, 4381, 545, 1090, 2180, 4360, 523, 1046, 2092, 4184, 171, 342, 684, 1368, 2736, 5472, 2779, 5558, 2935, 5870, 3527, 7054, 5895, 3605, 7210, 6223, 4229, 273, 546, 1092, 2184, 4368, 571, 1142, 2284, 4568, 939, 1878, 3756, 7512, 6827, 5453, 2689, 5378, 2591, 5182, 2151, 4302, 391, 782, 1564, 3128, 6256, 4347, 493, 986, 1972, 3944, 7888, 7611, 7021, 5825, 3481, 6962, 5759, 3301, 6602, 5007, 1797, 3594, 7188, 6195, 4221, 225, 450, 900, 1800, 3600, 7200, 6235, 4269, 321, 642, 1284, 2568, 5136, 2107, 4214, 247, 494, 988, 1976, 3952, 7904, 7643, 7085, 5953, 3737, 7474, 6783, 5349, 2513, 5026, 1887, 3774, 7548, 6883, 5597, 2977, 5954, 3743, 7486, 6759, 5333, 2481, 4962, 1759, 3518, 7036, 5859, 3549, 7098, 5999, 3781, 7562, 6927, 5637, 3089, 6178, 4191, 165, 330, 660, 1320, 2640, 5280, 2395, 4790, 1399, 2798, 5596, 2979, 5958, 3735, 7470, 6727, 5269, 2353, 4706, 1247, 2494, 4988, 1763, 3526, 7052, 5891, 3613, 7226, 6255, 4293, 401, 802, 1604, 3208, 6416, 4667, 1133, 2266, 4532, 883, 1766, 3532, 7064, 5931, 3661, 7322, 6447, 4677, 1169, 2338, 4676, 1171, 2342, 4684, 1155, 2310, 4620, 1027, 2054, 4108, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 4123, 45, 90, 180, 360, 720, 1440, 2880, 5760, 3355, 6710, 5239, 2293, 4586, 975, 1950, 3900, 7800, 7403, 6605, 4993, 1817, 3634, 7268, 6355, 4541, 865, 1730, 3460, 6920, 5643, 3085, 6170, 4143, 69, 138, 276, 552, 1104, 2208, 4416, 667, 1334, 2668, 5336, 2475, 4950, 1719, 3438, 6876, 5539, 2909, 5818, 3439, 6878, 5543, 2901, 5802, 3407, 6814, 5415, 2645, 5290, 2383, 4766, 1319, 2638, 5276, 2339, 4678, 1175, 2350, 4700, 1187, 2374, 4748, 1283, 2566, 5132, 2051, 4102, 23, 46, 92, 184, 368, 736, 1472, 2944, 5888, 3611, 7222, 6263, 4341, 497, 994, 1988, 3976, 7952, 7739, 7277, 6337, 4505, 809, 1618, 3236, 6472, 4747, 1293, 2586, 5172, 2163, 4326, 471, 942, 1884, 3768, 7536, 6907, 5613, 3009, 6018, 3871, 7742, 7271, 6357, 4529, 889, 1778, 3556, 7112, 6027, 3853, 7706, 7215, 6213, 4241, 313, 626, 1252, 2504, 5008, 1851, 3702, 7404, 6595, 5021, 1825, 3650, 7300, 6419, 4669, 1121, 2242, 4484, 787, 1574, 3148, 6296, 4395, 589, 1178, 2356, 4712, 1227, 2454, 4908, 1603, 3206, 6412, 4611, 1053, 2106, 4212, 243, 486, 972, 1944, 3888, 7776, 7387, 6573, 4929, 1689, 3378, 6756, 5331, 2493, 4986, 1775, 3550, 7100, 5987, 3805, 7610, 7023, 5829, 3473, 6946, 5727, 3237, 6474, 4751, 1285, 2570, 5140, 2099, 4198, 215, 430, 860, 1720, 3440, 6880, 5595, 2989, 5978, 3759, 7518, 6823, 5461, 2737, 5474, 2783, 5566, 2919, 5838, 3463, 6926, 5639, 3093, 6186, 4175, 133, 266, 532, 1064, 2128, 4256, 347, 694, 1388, 2776, 5552, 2939, 5878, 3575, 7150, 6087, 3989, 7978, 7759, 7301, 6417, 4665, 1129, 2258, 4516, 851, 1702, 3404, 6808, 5419, 2637, 5274, 2351, 4702, 1191, 2382, 4764, 1315, 2630, 5260, 2307, 4614, 1047, 2094, 4188, 163, 326, 652, 1304, 2608, 5216, 2267, 4534, 887, 1774, 3548, 7096, 5995, 3789, 7578, 6959, 5701, 3217, 6434, 4703, 1189, 2378, 4756, 1331, 2662, 5324, 2435, 4870, 1559, 3118, 6236, 4259, 349, 698, 1396, 2792, 5584, 3003, 6006, 3831, 7662, 7111, 6037, 3889, 7778, 7391, 6565, 4945, 1721, 3442, 6884, 5587, 3005, 6010, 3823, 7646, 7079, 5973, 3761, 7522, 6879, 5541, 2897, 5794, 3423, 6846, 5479, 2773, 5546, 2895, 5790, 3367, 6734, 5255, 2325, 4650, 1103, 2206, 4412, 611, 1222, 2444, 4888, 1579, 3158, 6316, 4419, 669, 1338, 2676, 5352, 2507, 5014, 1847, 3694, 7388, 6563, 4957, 1697, 3394, 6788, 5395, 2621, 5242, 2287, 4574, 935, 1870, 3740, 7480, 6763, 5325, 2433, 4866, 1567, 3134, 6268, 4323, 477, 954, 1908, 3816, 7632, 7099, 5997, 3777, 7554, 6943, 5669, 3153, 6306, 4447, 677, 1354, 2708, 5416, 2635, 5270, 2359, 4718, 1223, 2446, 4892, 1571, 3142, 6284, 4355, 541, 1082, 2164, 4328, 459, 918, 1836, 3672, 7344, 6523, 4845, 1473, 2946, 5892, 3603, 7206, 6231, 4277, 369, 738, 1476, 2952, 5904, 3643, 7286, 6391, 4597, 1009, 2018, 4036, 8072, 7947, 7693, 7169, 6169, 4137, 73, 146, 292, 584, 1168, 2336, 4672, 1179, 2358, 4716, 1219, 2438, 4876, 1539, 3078, 6156, 4099, 29, 58, 116, 232, 464, 928, 1856, 3712, 7424, 6683, 5165, 2113, 4226, 287, 574, 1148, 2296, 4592, 1019, 2038, 4076, 8152, 8107, 8013, 7809, 7449, 6697, 5193, 2185, 4370, 575, 1150, 2300, 4600, 1003, 2006, 4012, 8024, 7851, 7501, 6785, 5401, 2601, 5202, 2239, 4478, 743, 1486, 2972, 5944, 3691, 7382, 6583, 4981, 1777, 3554, 7108, 6035, 3901, 7802, 7407, 6597, 5009, 1849, 3698, 7396, 6611, 5053, 1889, 3778, 7556, 6931, 5693, 3169, 6338, 4511, 805, 1610, 3220, 6440, 4683, 1165, 2330, 4660, 1139, 2278, 4556, 899, 1798, 3596, 7192, 6187, 4173, 129, 258, 516, 1032, 2064, 4128, 91, 182, 364, 728, 1456, 2912, 5824, 3483, 6966, 5751, 3317, 6634, 5071, 1925, 3850, 7700, 7219, 6269, 4321, 473, 946, 1892, 3784, 7568, 6971, 5741, 3265, 6530, 4895, 1573, 3146, 6292, 4403, 637, 1274, 2548, 5096, 1995, 3990, 7980, 7747, 7325, 6433, 4697, 1193, 2386, 4772, 1363, 2726, 5452, 2691, 5382, 2583, 5166, 2119, 4238, 263, 526, 1052, 2104, 4208, 251, 502, 1004, 2008, 4016, 8032, 7899, 7597, 6977, 5785, 3369, 6738, 5311, 2405, 4810, 1423, 2846, 5692, 3171, 6342, 4503, 821, 1642, 3284, 6568, 4939, 1677, 3354, 6708, 5235, 2301, 4602, 1007, 2014, 4028, 8056, 7915, 7629, 7041, 5913, 3625, 7250, 6335, 4453, 721, 1442, 2884, 5768, 3339, 6678, 5175, 2165, 4330, 463, 926, 1852, 3704, 7408, 6651, 5101, 1985, 3970, 7940, 7699, 7229, 6241, 4313, 425, 850, 1700, 3400, 6800, 5435, 2669, 5338, 2479, 4958, 1703, 3406, 6812, 5411, 2653, 5306, 2415, 4830, 1447, 2894, 5788, 3363, 6726, 5271, 2357, 4714, 1231, 2462, 4924, 1635, 3270, 6540, 4867, 1565, 3130, 6260, 4339, 509, 1018, 2036, 4072, 8144, 8123, 8045, 7873, 7577, 6953, 5705, 3209, 6418, 4671, 1125, 2250, 4500, 819, 1638, 3276, 6552, 4907, 1613, 3226, 6452, 4723, 1277, 2554, 5108, 2035, 4070, 8140, 8067, 7965, 7713, 7257, 6313, 4425, 649, 1298, 2596, 5192, 2187, 4374, 567, 1134, 2268, 4536, 875, 1750, 3500, 7000, 5803, 3405, 6810, 5423, 2629, 5258, 2319, 4638, 1063, 2126, 4252, 291, 582, 1164, 2328, 4656, 1147, 2294, 4588, 963, 1926, 3852, 7704, 7211, 6221, 4225, 281, 562, 1124, 2248, 4496, 827, 1654, 3308, 6616, 5035, 1869, 3738, 7476, 6771, 5373, 2529, 5058, 1951, 3902, 7804, 7395, 6621, 5025, 1881, 3762, 7524, 6867, 5565, 2913, 5826, 3487, 6974, 5735, 3285, 6570, 4943, 1669, 3338, 6676, 5171, 2173, 4346, 495, 990, 1980, 3960, 7920, 7675, 7149, 6081, 3993, 7986, 7807, 7397, 6609, 5049, 1897, 3794, 7588, 6995, 5821, 3425, 6850, 5535, 2853, 5706, 3215, 6430, 4647, 1109, 2218, 4436, 691, 1382, 2764, 5528, 2859, 5718, 3255, 6510, 4807, 1429, 2858, 5716, 3251, 6502, 4823, 1461, 2922, 5844, 3507, 7014, 5847, 3509, 7018, 5839, 3461, 6922, 5647, 3077, 6154, 4111, 5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 2075, 4150, 119, 238, 476, 952, 1904, 3808, 7616, 7067, 5933, 3649, 7298, 6431, 4645, 1105, 2210, 4420, 659, 1318, 2636, 5272, 2347, 4694, 1207, 2414, 4828, 1443, 2886, 5772, 3331, 6662, 5143, 2101, 4202, 207, 414, 828, 1656, 3312, 6624, 5083, 1965, 3930, 7860, 7539, 6909, 5601, 3033, 6066, 3967, 7934, 7655, 7125, 6065, 3961, 7922, 7679, 7141, 6097, 4025, 8050, 7935, 7653, 7121, 6073, 3945, 7890, 7615, 7013, 5841, 3513, 7026, 5887, 3557, 7114, 6031, 3845, 7690, 7183, 6149, 4113, 57, 114, 228, 456, 912, 1824, 3648, 7296, 6427, 4653, 1089, 2178, 4356, 531, 1062, 2124, 4248, 299, 598, 1196, 2392, 4784, 1403, 2806, 5612, 3011, 6022, 3863, 7726, 7239, 6293, 4401, 633, 1266, 2532, 5064, 1931, 3862, 7724, 7235, 6301, 4385, 601, 1202, 2404, 4808, 1419, 2838, 5676, 3139, 6278, 4375, 565, 1130, 2260, 4520, 843, 1686, 3372, 6744, 5291, 2381, 4762, 1327, 2654, 5308, 2403, 4806, 1431, 2862, 5724, 3235, 6470, 4759, 1333, 2666, 5332, 2483, 4966, 1751, 3502, 7004, 5795, 3421, 6842, 5487, 2757, 5514, 2831, 5662, 3111, 6222, 4231, 277, 554, 1108, 2216, 4432, 699, 1398, 2796, 5592, 2987, 5974, 3767, 7534, 6855, 5525, 2865, 5730, 3295, 6590, 4967, 1749, 3498, 6996, 5811, 3453, 6906, 5615, 3013, 6026, 3855, 7710, 7207, 6229, 4273, 377, 754, 1508, 3016, 6032, 3899, 7798, 7415, 6645, 5105, 2041, 4082, 8164, 8147, 8125, 8033, 7897, 7593, 6985, 5769, 3337, 6674, 5183, 2149, 4298, 399, 798, 1596, 3192, 6384, 4603, 1005, 2010, 4020, 8040, 7883, 7565, 6913, 5657, 3113, 6226, 4287, 357, 714, 1428, 2856, 5712, 3259, 6518, 4855, 1525, 3050, 6100, 4019, 8038, 7895, 7605, 7025, 5881, 3561, 7122, 6079, 3941, 7882, 7567, 6917, 5649, 3129, 6258, 4351, 485, 970, 1940, 3880, 7760, 7355, 6509, 4801, 1433, 2866, 5732, 3283, 6566, 4951, 1717, 3434, 6868, 5555, 2941, 5882, 3567, 7134, 6055, 3925, 7850, 7503, 6789, 5393, 2617, 5234, 2303, 4606, 999, 1998, 3996, 7992, 7787, 7373, 6529, 4889, 1577, 3154, 6308, 4435, 701, 1402, 2804, 5608, 3019, 6038, 3895, 7790, 7367, 6549, 4913, 1657, 3314, 6628, 5075, 1981, 3962, 7924, 7667, 7165, 6113, 4057, 8114, 8063, 7909, 7633, 7097, 5993, 3785, 7570, 6975, 5733, 3281, 6562, 4959, 1701, 3402, 6804, 5427, 2685, 5370, 2543, 5086, 1959, 3918, 7836, 7459, 6749, 5281, 2393, 4786, 1407, 2814, 5628, 3043, 6086, 3991, 7982, 7751, 7317, 6449, 4729, 1257, 2514, 5028, 1875, 3750, 7500, 6787, 5405, 2593, 5186, 2207, 4414, 615, 1230, 2460, 4920, 1643, 3286, 6572, 4931, 1693, 3386, 6772, 5363, 2557, 5114, 2031, 4062, 8124, 8035, 7901, 7585, 7001, 5801, 3401, 6802, 5439, 2661, 5322, 2447, 4894, 1575, 3150, 6300, 4387, 605, 1210, 2420, 4840, 1483, 2966, 5932, 3651, 7302, 6423, 4661, 1137, 2274, 4548, 915, 1830, 3660, 7320, 6443, 4685, 1153, 2306, 4612, 1043, 2086, 4172, 131, 262, 524, 1048, 2096, 4192, 219, 438, 876, 1752, 3504, 7008, 5851, 3501, 7002, 5807, 3397, 6794, 5391, 2565, 5130, 2063, 4126, 39, 78, 156, 312, 624, 1248, 2496, 4992, 1819, 3638, 7276, 6339, 4509, 801, 1602, 3204, 6408, 4619, 1037, 2074, 4148, 115, 230, 460, 920, 1840, 3680, 7360, 6555, 4909, 1601, 3202, 6404, 4627, 1085, 2170, 4340, 499, 998, 1996, 3992, 7984, 7803, 7405, 6593, 5017, 1833, 3666, 7332, 6483, 4797, 1377, 2754, 5508, 2835, 5670, 3159, 6318, 4423, 661, 1322, 2644, 5288, 2379, 4758, 1335, 2670, 5340, 2467, 4934, 1687, 3374, 6748, 5283, 2397, 4794, 1391, 2782, 5564, 2915, 5830, 3479, 6958, 5703, 3221, 6442, 4687, 1157, 2314, 4628, 1075, 2150, 4300, 387, 774, 1548, 3096, 6192, 4219, 237, 474, 948, 1896, 3792, 7584, 7003, 5805, 3393, 6786, 5407, 2597, 5194, 2191, 4382, 551, 1102, 2204, 4408, 619, 1238, 2476, 4952, 1707, 3414, 6828, 5443, 2717, 5434, 2671, 5342, 2471, 4942, 1671, 3342, 6684, 5155, 2141, 4282, 367, 734, 1468, 2936, 5872, 3579, 7158, 6135, 4085, 8170, 8143, 8069, 7953, 7737, 7273, 6345, 4489, 777, 1554, 3108, 6216, 4235, 269, 538, 1076, 2152, 4304, 443, 886, 1772, 3544, 7088, 6011, 3821, 7642, 7087, 5957, 3729, 7458, 6751, 5285, 2385, 4770, 1375, 2750, 5500, 2787, 5574, 2967, 5934, 3655, 7310, 6407, 4629, 1073, 2146, 4292, 403, 806, 1612, 3224, 6448, 4731, 1261, 2522, 5044, 1907, 3814, 7628, 7043, 5917, 3617, 7234, 6303, 4389, 593, 1186, 2372, 4744, 1291, 2582, 5164, 2115, 4230, 279, 558, 1116, 2232, 4464, 763, 1526, 3052, 6104, 4011, 8022, 7863, 7541, 6897, 5625, 3049, 6098, 4031, 8062, 7911, 7637, 7089, 6009, 3817, 7634, 7103, 5989, 3793, 7586, 7007, 5797, 3409, 6818, 5471, 2725, 5450, 2703, 5406, 2599, 5198, 2183, 4366, 519, 1038, 2076, 4152, 107, 214, 428, 856, 1712, 3424, 6848, 5531, 2861, 5722, 3247, 6494, 4775, 1365, 2730, 5460, 2739, 5478, 2775, 5550, 2887, 5774, 3335, 6670, 5127, 2069, 4138, 79, 158, 316, 632, 1264, 2528, 5056, 1947, 3894, 7788, 7363, 6557, 4897, 1625, 3250, 6500, 4819, 1469, 2938, 5876, 3571, 7142, 6103, 4021, 8042, 7887, 7557, 6929, 5689, 3177, 6354, 4543, 869, 1738, 3476, 6952, 5707, 3213, 6426, 4655, 1093, 2186, 4372, 563, 1126, 2252, 4504, 811, 1622, 3244, 6488, 4779, 1357, 2714, 5428, 2675, 5350, 2519, 5038, 1863, 3726, 7452, 6691, 5213, 2209, 4418, 671, 1342, 2684, 5368, 2539, 5078, 1975, 3950, 7900, 7587, 7005, 5793, 3417, 6834, 5503, 2789, 5578, 2959, 5918, 3623, 7246, 6279, 4373, 561, 1122, 2244, 4488, 779, 1558, 3116, 6232, 4267, 333, 666, 1332, 2664, 5328, 2491, 4982, 1783, 3566, 7132, 6051, 3933, 7866, 7535, 6853, 5521, 2873, 5746, 3327, 6654, 5095, 2005, 4010, 8020, 7859, 7549, 6881, 5593, 2985, 5970, 3775, 7550, 6887, 5589, 2993, 5986, 3807, 7614, 7015, 5845, 3505, 7010, 5855, 3493, 6986, 5775, 3333, 6666, 5135, 2053, 4106, 15, 30, 60, 120, 240, 480, 960, 1920, 3840, 7680, 7195, 6189, 4161, 153, 306, 612, 1224, 2448, 4896, 1627, 3254, 6508, 4803, 1437, 2874, 5748, 3315, 6630, 5079, 1973, 3946, 7892, 7603, 7037, 5857, 3545, 7090, 6015, 3813, 7626, 7055, 5893, 3601, 7202, 6239, 4261, 337, 674, 1348, 2696, 5392, 2619, 5238, 2295, 4590, 967, 1934, 3868, 7736, 7275, 6349, 4481, 793, 1586, 3172, 6344, 4491, 781, 1562, 3124, 6248, 4299, 397, 794, 1588, 3176, 6352, 4539, 877, 1754, 3508, 7016, 5835, 3469, 6938, 5679, 3141, 6282, 4367, 517, 1034, 2068, 4136, 75, 150, 300, 600, 1200, 2400, 4800, 1435, 2870, 5740, 3267, 6534, 4887, 1589, 3178, 6356, 4531, 893, 1786, 3572, 7144, 6091, 3981, 7962, 7727, 7237, 6289, 4409, 617, 1234, 2468, 4936, 1675, 3350, 6700, 5187, 2205, 4410, 623, 1246, 2492, 4984, 1771, 3542, 7084, 5955, 3741, 7482, 6767, 5317, 2449, 4898, 1631, 3262, 6524, 4835, 1501, 3002, 6004, 3827, 7654, 7127, 6069, 3953, 7906, 7647, 7077, 5969, 3769, 7538, 6911, 5605, 3025, 6050, 3935, 7870, 7527, 6869, 5553, 2937, 5874, 3583, 7166, 6119, 4053, 8106, 8015, 7813, 7441, 6713, 5225, 2249, 4498, 831, 1662, 3324, 6648, 5099, 1997, 3994, 7988, 7795, 7421, 6625, 5081, 1961, 3922, 7844, 7507, 6845, 5473, 2777, 5554, 2943, 5886, 3559, 7118, 6023, 3861, 7722, 7247, 6277, 4369, 569, 1138, 2276, 4552, 907, 1814, 3628, 7256, 6315, 4429, 641, 1282, 2564, 5128, 2059, 4118, 55, 110, 220, 440, 880, 1760, 3520, 7040, 5915, 3629, 7258, 6319, 4421, 657, 1314, 2628, 5256, 2315, 4630, 1079, 2158, 4316, 419, 838, 1676, 3352, 6704, 5243, 2285, 4570, 943, 1886, 3772, 7544, 6891, 5581, 2945, 5890, 3615, 7230, 6247, 4309, 433, 866, 1732, 3464, 6928, 5691, 3181, 6362, 4527, 837, 1674, 3348, 6696, 5195, 2189, 4378, 559, 1118, 2236, 4472, 747, 1494, 2988, 5976, 3755, 7510, 6839, 5493, 2801, 5602, 3039, 6078, 3943, 7886, 7559, 6933, 5681, 3193, 6386, 4607, 997, 1994, 3988, 7976, 7755, 7309, 6401, 4633, 1065, 2130, 4260, 339, 678, 1356, 2712, 5424, 2683, 5366, 2551, 5102, 1991, 3982, 7964, 7715, 7261, 6305, 4441, 681, 1362, 2724, 5448, 2699, 5398, 2615, 5230, 2247, 4494, 775, 1550, 3100, 6200, 4203, 205, 410, 820, 1640, 3280, 6560, 4955, 1709, 3418, 6836, 5491, 2813, 5626, 3055, 6110, 4007, 8014, 7815, 7445, 6705, 5241, 2281, 4562, 959, 1918, 3836, 7672, 7147, 6093, 3969, 7938, 7711, 7205, 6225, 4281, 361, 722, 1444, 2888, 5776, 3387, 6774, 5367, 2549, 5098, 1999, 3998, 7996, 7779, 7389, 6561, 4953, 1705, 3410, 6820, 5459, 2749, 5498, 2799, 5598, 2983, 5966, 3719, 7438, 6663, 5141, 2097, 4194, 223, 446, 892, 1784, 3568, 7136, 6107, 4013, 8026, 7855, 7493, 6801, 5433, 2665, 5330, 2495, 4990, 1767, 3534, 7068, 5923, 3677, 7354, 6511, 4805, 1425, 2850, 5700, 3219, 6438, 4695, 1205, 2410, 4820, 1459, 2918, 5836, 3459, 6918, 5655, 3125, 6250, 4303, 389, 778, 1556, 3112, 6224, 4283, 365, 730, 1460, 2920, 5840, 3515, 7030, 5879, 3573, 7146, 6095, 3973, 7946, 7695, 7173, 6161, 4153, 105, 210, 420, 840, 1680, 3360, 6720, 5275, 2349, 4698, 1199, 2398, 4796, 1379, 2758, 5516, 2819, 5638, 3095, 6190, 4167, 149, 298, 596, 1192, 2384, 4768, 1371, 2742, 5484, 2755, 5510, 2839, 5678, 3143, 6286, 4359, 533, 1066, 2132, 4264, 331, 662, 1324, 2648, 5296, 2427, 4854, 1527, 3054, 6108, 4003, 8006, 7831, 7477, 6769, 5369, 2537, 5074, 1983, 3966, 7932, 7651, 7133, 6049, 3929, 7858, 7551, 6885, 5585, 3001, 6002, 3839, 7678, 7143, 6101, 4017, 8034, 7903, 7589, 6993, 5817, 3433, 6866, 5567, 2917, 5834, 3471, 6942, 5671, 3157, 6314, 4431, 645, 1290, 2580, 5160, 2123, 4246, 311, 622, 1244, 2488, 4976, 1787, 3574, 7148, 6083, 3997, 7994, 7791, 7365, 6545, 4921, 1641, 3282, 6564, 4947, 1725, 3450, 6900, 5619, 3069, 6138, 4079, 8158, 8103, 8021, 7857, 7545, 6889, 5577, 2953, 5906, 3647, 7294, 6375, 4565, 945, 1890, 3780, 7560, 6923, 5645, 3073, 6146, 4127, 37, 74, 148, 296, 592, 1184, 2368, 4736, 1307, 2614, 5228, 2243, 4486, 791, 1582, 3164, 6328, 4459, 717, 1434, 2868, 5736, 3275, 6550, 4919, 1653, 3306, 6612, 5043, 1917, 3834, 7668, 7155, 6141, 4065, 8130, 8095, 7973, 7761, 7353, 6505, 4809, 1417, 2834, 5668, 3155, 6310, 4439, 693, 1386, 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6623, 5029, 1873, 3746, 7492, 6803, 5437, 2657, 5314, 2463, 4926, 1639, 3278, 6556, 4899, 1629, 3258, 6516, 4851, 1533, 3066, 6132, 4083, 8166, 8151, 8117, 8049, 7929, 7657, 7113, 6025, 3849, 7698, 7231, 6245, 4305, 441, 882, 1764, 3528, 7056, 5947, 3693, 7386, 6575, 4933, 1681, 3362, 6724, 5267, 2365, 4730, 1263, 2526, 5052, 1891, 3782, 7564, 6915, 5661, 3105, 6210, 4255, 293, 586, 1172, 2344, 4688, 1211, 2422, 4844, 1475, 2950, 5900, 3587, 7174, 6167, 4149, 113, 226, 452, 904, 1808, 3616, 7232, 6299, 4397, 577, 1154, 2308, 4616, 1035, 2070, 4140, 67, 134, 268, 536, 1072, 2144, 4288, 411, 822, 1644, 3288, 6576, 4987, 1773, 3546, 7092, 6003, 3837, 7674, 7151, 6085, 3985, 7970, 7775, 7333, 6481, 4793, 1385, 2770, 5540, 2899, 5798, 3415, 6830, 5447, 2709, 5418, 2639, 5278, 2343, 4686, 1159, 2318, 4636, 1059, 2118, 4236, 259, 518, 1036, 2072, 4144, 123, 246, 492, 984, 1968, 3936, 7872, 7579, 6957, 5697, 3225, 6450, 4735, 1253, 2506, 5012, 1843, 3686, 7372, 6531, 4893, 1569, 3138, 6276, 4371, 573, 1146, 2292, 4584, 971, 1942, 3884, 7768, 7339, 6477, 4737, 1305, 2610, 5220, 2259, 4518, 855, 1710, 3420, 6840, 5483, 2765, 5530, 2863, 5726, 3239, 6478, 4743, 1301, 2602, 5204, 2227, 4454, 727, 1454, 2908, 5816, 3435, 6870, 5559, 2933, 5866, 3535, 7070, 5927, 3669, 7338, 6479, 4741, 1297, 2594, 5188, 2195, 4390, 599, 1198, 2396, 4792, 1387, 2774, 5548, 2883, 5766, 3351, 6702, 5191, 2197, 4394, 591, 1182, 2364, 4728, 1259, 2518, 5036, 1859, 3718, 7436, 6659, 5149, 2081, 4162, 159, 318, 636, 1272, 2544, 5088, 2011, 4022, 8044, 7875, 7581, 6945, 5721, 3241, 6482, 4799, 1381, 2762, 5524, 2867, 5734, 3287, 6574, 4935, 1685, 3370, 6740, 5299, 2429, 4858, 1519, 3038, 6076, 3939, 7878, 7575, 6965, 5745, 3321, 6642, 5119, 2021, 4042, 8084, 7987, 7805, 7393, 6617, 5033, 1865, 3730, 7460, 6739, 5309, 2401, 4802, 1439, 2878, 5756, 3299, 6598, 5015, 1845, 3690, 7380, 6579, 4989, 1761, 3522, 7044, 5907, 3645, 7290, 6383, 4549, 913, 1826, 3652, 7304, 6411, 4621, 1025, 2050, 4100, 19, 38, 76, 152, 304, 608, 1216, 2432, 4864, 1563, 3126, 6252, 4291, 413, 826, 1652, 3304, 6608, 5051, 1901, 3802, 7604, 7027, 5885, 3553, 7106, 6047, 3877, 7754, 7311, 6405, 4625, 1081, 2162, 4324, 467, 934, 1868, 3736, 7472, 6779, 5357, 2497, 4994, 1823, 3646, 7292, 6371, 4573, 929, 1858, 3716, 7432, 6667, 5133, 2049, 4098, 31, 62, 124, 248, 496, 992, 1984, 3968, 7936, 7707, 7213, 6209, 4249, 297, 594, 1188, 2376, 4752, 1339, 2678, 5356, 2499, 4998, 1815, 3630, 7260, 6307, 4445, 673, 1346, 2692, 5384, 2571, 5142, 2103, 4206, 199, 398, 796, 1592, 3184, 6368, 4571, 941, 1882, 3764, 7528, 6859, 5517, 2817, 5634, 3103, 6206, 4199, 213, 426, 852, 1704, 3408, 6816, 5467, 2733, 5466, 2735, 5470, 2727, 5454, 2695, 5390, 2567, 5134, 2055, 4110, 7, 14, 28, 56, 112, 224, 448, 896, 1792, 3584, 7168, 6171, 4141, 65, 130, 260, 520, 1040, 2080, 4160, 155, 310, 620, 1240, 2480, 4960, 1755, 3510, 7020, 5827, 3485, 6970, 5743, 3269, 6538, 4879, 1541, 3082, 6164, 4147, 125, 250, 500, 1000, 2000, 4000, 8000, 7835, 7469, 6721, 5273, 2345, 4690, 1215, 2430, 4860, 1507, 3014, 6028, 3843, 7686, 7191, 6197, 4209, 249, 498, 996, 1992, 3984, 7968, 7771, 7341, 6465, 4761, 1321, 2642, 5284, 2387, 4774, 1367, 2734, 5468, 2723, 5446, 2711, 5422, 2631, 5262, 2311, 4622, 1031, 2062, 4124, 35, 70, 140, 280, 560, 1120, 2240, 4480, 795, 1590, 3180, 6360, 4523, 845, 1690, 3380, 6760, 5323, 2445, 4890, 1583, 3166, 6332, 4451, 733, 1466, 2932, 5864, 3531, 7062, 5943, 3701, 7402, 6607, 4997, 1809, 3618, 7236, 6291, 4413, 609, 1218, 2436, 4872, 1547, 3094, 6188, 4163, 157, 314, 628, 1256, 2512, 5024, 1883, 3766, 7532, 6851, 5533, 2849, 5698, 3231, 6462, 4711, 1237, 2474, 4948, 1715, 3430, 6860, 5507, 2845, 5690, 3183, 6366, 4519, 853, 1706, 3412, 6824, 5451, 2701, 5402, 2607, 5214, 2215, 4430, 647, 1294, 2588, 5176, 2155, 4310, 439, 878, 1756, 3512, 7024, 5883, 3565, 7130, 6063, 3909, 7818, 7439, 6661, 5137, 2105, 4210, 255, 510, 1020, 2040, 4080, 8160, 8155, 8109, 8001, 7833, 7465, 6729, 5257, 2313, 4626, 1087, 2174, 4348, 483, 966, 1932, 3864, 7728, 7291, 6381, 4545, 921, 1842, 3684, 7368, 6539, 4877, 1537, 3074, 6148, 4115, 61, 122, 244, 488, 976, 1952, 3904, 7808, 7451, 6701, 5185, 2201, 4402, 639, 1278, 2556, 5112, 2027, 4054, 8108, 8003, 7837, 7457, 6745, 5289, 2377, 4754, 1343, 2686, 5372, 2531, 5062, 1943, 3886, 7772, 7331, 6493, 4769, 1369, 2738, 5476, 2771, 5542, 2903, 5806, 3399, 6798, 5383, 2581, 5162, 2127, 4254, 295, 590, 1180, 2360, 4720, 1275, 2550, 5100, 1987, 3974, 7948, 7683, 7197, 6177, 4185, 169, 338, 676, 1352, 2704, 5408, 2651, 5302, 2423, 4846, 1479, 2958, 5916, 3619, 7238, 6295, 4405, 625, 1250, 2500, 5000, 1803, 3606, 7212, 6211, 4253, 289, 578, 1156, 2312, 4624, 1083, 2166, 4332, 451, 902, 1804, 3608, 7216, 6267, 4333, 449, 898, 1796, 3592, 7184, 6203, 4205, 193, 386, 772, 1544, 3088, 6176, 4187, 173, 346, 692, 1384, 2768, 5536, 2907, 5814, 3447, 6894, 5575, 2965, 5930, 3663, 7326, 6439, 4693, 1201, 2402, 4804, 1427, 2854, 5708, 3203, 6406, 4631, 1077, 2154, 4308, 435, 870, 1740, 3480, 6960, 5755, 3309, 6618, 5039, 1861, 3722, 7444, 6707, 5245, 2273, 4546, 927, 1854, 3708, 7416, 6635, 5069, 1921, 3842, 7684, 7187, 6205, 4193, 217, 434, 868, 1736, 3472, 6944, 5723, 3245, 6490, 4783, 1349, 2698, 5396, 2611, 5222, 2263, 4526, 839, 1678, 3356, 6712, 5227, 2253, 4506, 815, 1630, 3260, 6520, 4843, 1485, 2970, 5940, 3699, 7398, 6615, 5045, 1905, 3810, 7620, 7059, 5949, 3681, 7362, 6559, 4901, 1617, 3234, 6468, 4755, 1341, 2682, 5364, 2547, 5094, 2007, 4014, 8028, 7843, 7517, 6817, 5465, 2729, 5458, 2751, 5502, 2791, 5582, 2951, 5902, 3591, 7182, 6151, 4117, 49, 98, 196, 392, 784, 1568, 3136, 6272, 4379, 557, 1114, 2228, 4456, 715, 1430, 2860, 5720, 3243, 6486, 4791, 1397, 2794, 5588, 2995, 5990, 3799, 7598, 6983, 5781, 3377, 6754, 5343, 2469, 4938, 1679, 3358, 6716, 5219, 2269, 4538, 879, 1758, 3516, 7032, 5867, 3533, 7066, 5935, 3653, 7306, 6415, 4613, 1041, 2082, 4164, 147, 294, 588, 1176, 2352, 4704, 1243, 2486, 4972, 1731, 3462, 6924, 5635, 3101, 6202, 4207, 197, 394, 788, 1576, 3152, 6304, 4443, 685, 1370, 2740, 5480, 2763, 5526, 2871, 5742, 3271, 6542, 4871, 1557, 3114, 6228, 4275, 381, 762, 1524, 3048, 6096, 4027, 8054, 7927, 7669, 7153, 6137, 4073, 8146, 8127, 8037, 7889, 7609, 7017, 5833, 3465, 6930, 5695, 3173, 6346, 4495, 773, 1546, 3092, 6184, 4171, 141, 282, 564, 1128, 2256, 4512, 859, 1718, 3436, 6872, 5547, 2893, 5786, 3375, 6750, 5287, 2389, 4778, 1359, 2718, 5436, 2659, 5318, 2455, 4910, 1607, 3214, 6428, 4643, 1117, 2234, 4468, 755, 1510, 3020, 6040, 3883, 7766, 7351, 6517, 4849, 1529, 3058, 6116, 4051, 8102, 8023, 7861, 7537, 6905, 5609, 3017, 6034, 3903, 7806, 7399, 6613, 5041, 1913, 3826, 7652, 7123, 6077, 3937, 7874, 7583, 6949, 5713, 3257, 6514, 4863, 1509, 3018, 6036, 3891, 7782, 7383, 6581, 4977, 1785, 3570, 7140, 6099, 4029, 8058, 7919, 7621, 7057, 5945, 3689, 7378, 6591, 4965, 1745, 3490, 6980, 5779, 3389, 6778, 5359, 2501, 5002, 1807, 3614, 7228, 6243, 4317, 417, 834, 1668, 3336, 6672, 5179, 2157, 4314, 431, 862, 1724, 3448, 6896, 5627, 3053, 6106, 4015, 8030, 7847, 7509, 6833, 5497, 2793, 5586, 3007, 6014, 3815, 7630, 7047, 5909, 3633, 7266, 6367, 4517, 849, 1698, 3396, 6792, 5387, 2573, 5146, 2095, 4190, 167, 334, 668, 1336, 2672, 5344, 2523, 5046, 1911, 3822, 7644, 7075, 5981, 3745, 7490, 6815, 5413, 2641, 5282, 2399, 4798, 1383, 2766, 5532, 2851, 5702, 3223, 6446, 4679, 1173, 2346, 4692, 1203, 2406, 4812, 1411, 2822, 5644, 3075, 6150, 4119, 53, 106, 212, 424, 848, 1696, 3392, 6784, 5403, 2605, 5210, 2223, 4446, 679, 1358, 2716, 5432, 2667, 5334, 2487, 4974, 1735, 3470, 6940, 5667, 3165, 6330, 4463, 709, 1418, 2836, 5672, 3147, 6294, 4407, 629, 1258, 2516, 5032, 1867, 3734, 7468, 6723, 5277, 2337, 4674, 1183, 2366, 4732, 1251, 2502, 5004, 1795, 3590, 7180, 6147, 4125, 33, 66, 132, 264, 528, 1056, 2112, 4224, 283, 566, 1132, 2264, 4528, 891, 1782, 3564, 7128, 6059, 3917, 7834, 7471, 6725, 5265, 2361, 4722, 1279, 2558, 5116, 2019, 4038, 8076, 7939, 7709, 7201, 6233, 4265, 329, 658, 1316, 2632, 5264, 2363, 4726, 1271, 2542, 5084, 1955, 3910, 7820, 7427, 6685, 5153, 2137, 4274, 383, 766, 1532, 3064, 6128, 4091, 8182, 8183, 8181, 8177, 8185, 8169, 8137, 8073, 7945, 7689, 7177, 6153, 4105, 9, 18, 36, 72, 144, 288, 576, 1152, 2304, 4608, 1051, 2102, 4204, 195, 390, 780, 1560, 3120, 6240, 4315, 429, 858, 1716, 3432, 6864, 5563, 2925, 5850, 3503, 7006, 5799, 3413, 6826, 5455, 2693, 5386, 2575, 5150, 2087, 4174, 135, 270, 540, 1080, 2160, 4320, 475, 950, 1900, 3800, 7600, 7035, 5869, 3521, 7042, 5919, 3621, 7242, 6287, 4357, 529, 1058, 2116, 4232, 267, 534, 1068, 2136, 4272, 379, 758, 1516, 3032, 6064, 3963, 7926, 7671, 7157, 6129, 4089, 8178, 8191, 8165, 8145, 8121, 8041, 7881, 7561, 6921, 5641, 3081, 6162, 4159, 101, 202, 404, 808, 1616, 3232, 6464, 4763, 1325, 2650, 5300, 2419, 4838, 1495, 2990, 5980, 3747, 7494, 6807, 5429, 2673, 5346, 2527, 5054, 1895, 3790, 7580, 6947, 5725, 3233, 6466, 4767, 1317, 2634, 5268, 2355, 4710, 1239, 2478, 4956, 1699, 3398, 6796, 5379, 2589, 5178, 2159, 4318, 423, 846, 1692, 3384, 6768, 5371, 2541, 5082, 1967, 3934, 7868, 7523, 6877, 5537, 2905, 5810, 3455, 6910, 5607, 3029, 6058, 3919, 7838, 7463, 6741, 5297, 2425, 4850, 1535, 3070, 6140, 4067, 8134, 8087, 7989, 7793, 7417, 6633, 5065, 1929, 3858, 7716, 7251, 6333, 4449, 729, 1458, 2916, 5832, 3467, 6934, 5687, 3189, 6378, 4559, 901, 1802, 3604, 7208, 6219, 4237, 257, 514, 1028, 2056, 4112, 59, 118, 236, 472, 944, 1888, 3776, 7552, 6939, 5677, 3137, 6274, 4383, 549, 1098, 2196, 4392, 587, 1174, 2348, 4696, 1195, 2390, 4780, 1347, 2694, 5388, 2563, 5126, 2071, 4142, 71, 142, 284, 568, 1136, 2272, 4544, 923, 1846, 3692, 7384, 6571, 4941, 1665, 3330, 6660, 5139, 2109, 4218, 239, 478, 956, 1912, 3824, 7648, 7131, 6061, 3905, 7810, 7455, 6693, 5201, 2233, 4466, 767, 1534, 3068, 6136, 4075, 8150, 8119, 8053, 7921, 7673, 7145, 6089, 3977, 7954, 7743, 7269, 6353, 4537, 873, 1746, 3492, 6984, 5771, 3341, 6682, 5167, 2117, 4234, 271, 542, 1084, 2168, 4336, 507, 1014, 2028, 4056, 8112, 8059, 7917, 7617, 7065, 5929, 3657, 7314, 6463, 4709, 1233, 2466, 4932, 1683, 3366, 6732, 5251, 2333, 4666, 1135, 2270, 4540, 867, 1734, 3468, 6936, 5675, 3149, 6298, 4399, 581, 1162, 2324, 4648, 1099, 2198, 4396, 579, 1158, 2316, 4632, 1067, 2134, 4268, 323, 646, 1292, 2584, 5168, 2171, 4342, 503, 1006, 2012, 4024, 8048, 7931, 7661, 7105, 6041, 3881, 7762, 7359, 6501, 4817, 1465, 2930, 5860, 3539, 7078, 5975, 3765, 7530, 6863, 5509, 2833, 5666, 3167, 6334, 4455, 725, 1450, 2900, 5800, 3403, 6806, 5431, 2677, 5354, 2511, 5022, 1831, 3662, 7324, 6435, 4701, 1185, 2370, 4740, 1299, 2598, 5196, 2179, 4358, 535, 1070, 2140, 4280, 363, 726, 1452, 2904, 5808, 3451, 6902, 5623, 3061, 6122, 4047, 8094, 7975, 7765, 7345, 6521, 4841, 1481, 2962, 5924, 3667, 7334, 6487, 4789, 1393, 2786, 5572, 2963, 5926, 3671, 7342, 6471, 4757, 1329, 2658, 5316, 2451, 4902, 1623, 3246, 6492, 4771, 1373, 2746, 5492, 2803, 5606, 3031, 6062, 3911, 7822, 7431, 6677, 5169, 2169, 4338, 511, 1022, 2044, 4088, 8176, 8187, 8173, 8129, 8089, 7977, 7753, 7305, 6409, 4617, 1033, 2066, 4132, 83, 166, 332, 664, 1328, 2656, 5312, 2459, 4918, 1655, 3310, 6620, 5027, 1885, 3770, 7540, 6899, 5629, 3041, 6082, 3999, 7998, 7783, 7381, 6577, 4985, 1769, 3538, 7076, 5971, 3773, 7546, 6895, 5573, 2961, 5922, 3679, 7358, 6503, 4821, 1457, 2914, 5828, 3475, 6950, 5719, 3253, 6506, 4815, 1413, 2826, 5652, 3123, 6246, 4311, 437, 874, 1748, 3496, 6992, 5819, 3437, 6874, 5551, 2885, 5770, 3343, 6686, 5159, 2133, 4266, 335, 670, 1340, 2680, 5360, 2555, 5110, 2039, 4078, 8156, 8099, 8029, 7841, 7513, 6825, 5449, 2697, 5394, 2623, 5246, 2279, 4558, 903, 1806, 3612, 7224, 6251, 4301, 385, 770, 1540, 3080, 6160, 4155, 109, 218, 436, 872, 1744, 3488, 6976, 5787, 3373, 6746, 5295, 2373, 4746, 1295, 2590, 5180, 2147, 4294, 407, 814, 1628, 3256, 6512, 4859, 1517, 3034, 6068, 3955, 7910, 7639, 7093, 6001, 3833, 7666, 7167, 6117, 4049, 8098, 8031, 7845, 7505, 6841, 5481, 2761, 5522, 2879, 5758, 3303, 6606, 4999, 1813, 3626, 7252, 6323, 4477, 737, 1474, 2948, 5896, 3595, 7190, 6199, 4213, 241, 482, 964, 1928, 3856, 7712, 7259, 6317, 4417, 665, 1330, 2660, 5320, 2443, 4886, 1591, 3182, 6364, 4515, 861, 1722, 3444, 6888, 5579, 2957, 5914, 3631, 7262, 6311, 4437, 689, 1378, 2756, 5512, 2827, 5654, 3127, 6254, 4295, 405, 810, 1620, 3240, 6480, 4795, 1389, 2778, 5556, 2931, 5862, 3543, 7086, 5959, 3733, 7466, 6735, 5253, 2321, 4642, 1119, 2238, 4476, 739, 1478, 2956, 5912, 3627, 7254, 6327, 4469, 753, 1506, 3012, 6024, 3851, 7702, 7223, 6261, 4337, 505, 1010, 2020, 4040, 8080, 7995, 7789, 7361, 6553, 4905, 1609, 3218, 6436, 4691, 1213, 2426, 4852, 1523, 3046, 6092, 3971, 7942, 7703, 7221, 6257, 4345, 489, 978, 1956, 3912, 7824, 7483, 6765, 5313, 2457, 4914, 1663, 3326, 6652, 5091, 2013, 4026, 8052, 7923, 7677, 7137, 6105, 4009, 8018, 7871, 7525, 6865, 5561, 2921, 5842, 3519, 7038, 5863, 3541, 7082, 5967, 3717, 7434, 6671, 5125, 2065, 4130, 95, 190, 380, 760, 1520, 3040, 6080, 3995, 7990, 7799, 7413, 6641, 5113, 2025, 4050, 8100, 8019, 7869, 7521, 6873, 5545, 2889, 5778, 3391, 6782, 5351, 2517, 5034, 1871, 3742, 7484, 6755, 5341, 2465, 4930, 1695, 3390, 6780, 5347, 2525, 5050, 1903, 3806, 7612, 7011, 5853, 3489, 6978, 5791, 3365, 6730, 5263, 2309, 4618, 1039, 2078, 4156, 99, 198, 396, 792, 1584, 3168, 6336, 4507, 813, 1626, 3252, 6504, 4811, 1421, 2842, 5684, 3187, 6374, 4567, 949, 1898, 3796, 7592, 6987, 5773, 3329, 6658, 5151, 2085, 4170, 143, 286, 572, 1144, 2288, 4576, 987, 1974, 3948, 7896, 7595, 6989, 5761, 3353, 6706, 5247, 2277, 4554, 911, 1822, 3644, 7288, 6379, 4557, 897, 1794, 3588, 7176, 6155, 4109, 1}; +typedef Field Field13; + +// 14 bit field +typedef RecLinTrans StatTable14; +constexpr StatTable14 QRT_TABLE_14({5106, 518, 516, 15878, 512, 4710, 15886, 276, 528, 0, 4678, 10312, 15950, 8792}); +constexpr uint16_t LOG_TABLE_14[] = {16383, 0, 7755, 5757, 15510, 11514, 13512, 1, 6882, 5758, 2886, 2414, 4884, 3025, 7756, 888, 14637, 6645, 13513, 2091, 10641, 2, 10169, 8782, 12639, 188, 10780, 11515, 15511, 8171, 8643, 4515, 6009, 10272, 14400, 3026, 4885, 5776, 9846, 13928, 2013, 12188, 7757, 5945, 1541, 889, 154, 14932, 4011, 2415, 7943, 12402, 2152, 7848, 2887, 10196, 6883, 14539, 15926, 16331, 15, 4999, 12270, 5759, 13764, 11516, 1644, 12552, 5772, 4828, 10781, 10756, 12640, 4616, 13531, 3913, 1218, 5705, 5300, 189, 9768, 6050, 3560, 8172, 15512, 1776, 13700, 13266, 9296, 15953, 8644, 13848, 7909, 4516, 6304, 13605, 11766, 10671, 10170, 16029, 15698, 8783, 3774, 6952, 9907, 3302, 15603, 3, 10642, 5597, 1568, 11533, 14638, 4306, 5911, 2607, 7298, 4256, 7703, 6646, 7770, 2092, 12754, 1562, 3642, 11702, 13514, 5439, 5136, 11196, 2888, 10634, 9399, 10197, 3924, 1076, 13527, 5883, 12583, 7849, 2153, 7319, 2128, 3649, 4012, 14075, 12371, 10063, 4903, 8364, 11668, 2416, 8973, 12403, 13460, 7540, 13055, 3518, 7944, 10013, 1140, 16332, 13805, 45, 11315, 5403, 15927, 13522, 6884, 12709, 9531, 15654, 5072, 4505, 4638, 14540, 668, 907, 7325, 5000, 16, 3213, 5220, 11354, 15664, 5977, 12271, 9059, 14059, 5760, 4977, 7182, 3138, 411, 2043, 890, 1542, 1926, 7401, 5116, 7070, 130, 155, 9480, 11529, 14933, 14707, 10585, 1279, 5946, 11057, 10131, 6975, 6685, 7758, 11462, 2014, 6929, 13352, 10373, 9323, 9670, 2905, 12189, 6010, 2979, 12061, 2602, 13666, 2211, 10362, 10273, 15053, 3027, 12011, 5327, 15458, 3222, 14401, 4049, 15525, 9359, 9847, 11807, 4126, 13929, 9317, 10041, 11397, 2640, 3074, 5777, 4886, 9472, 13194, 7533, 12891, 13290, 2568, 5598, 10643, 4182, 2006, 15229, 771, 963, 1569, 8397, 11679, 11534, 8831, 2973, 4899, 4, 13638, 15116, 3955, 1181, 15604, 4703, 9908, 15798, 15074, 14661, 9883, 13570, 11404, 3303, 11767, 8024, 5447, 8736, 3743, 8359, 1435, 10672, 12658, 16030, 16119, 14012, 3040, 11024, 10171, 7968, 345, 9806, 3775, 14602, 4832, 6953, 15295, 8979, 4427, 13323, 11273, 8784, 15699, 11084, 1385, 2240, 8895, 376, 7704, 6168, 5177, 6647, 7800, 8190, 2687, 10873, 13158, 4257, 7299, 7198, 4894, 7683, 14639, 16342, 4081, 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427, 13856, 5808, 10818, 14220, 14896, 12135, 10451, 4803, 629, 1794, 101, 9185, 2131, 5392, 3333, 3242, 14282, 6126, 12775, 123, 15517, 15880, 10418, 6542, 7292, 10943, 3658, 13371, 12202, 14769, 10698, 6462, 13951, 13087, 12244, 1397, 7927, 3908, 6569, 932, 1083, 5368, 9570, 11893, 7229, 8250, 6958, 8427, 2559, 6146, 446, 3652, 13942, 14035, 6855, 7263, 9092, 9214, 1640, 13217, 8096, 13721, 13258, 10774, 5956, 4339, 10430, 11359, 5732, 9251, 4456, 3880, 12208, 2295, 3747, 6351, 1209, 16296, 6158, 5835, 3692, 6770, 3015, 8744, 11284, 14378, 13224, 13875, 9521, 6346, 5318, 9001, 8573, 11847, 6749, 8261, 6023, 1445, 1373, 1963, 2022, 9342, 8001, 582, 539, 663, 3391, 13550, 3159, 651, 14617, 3703, 4580, 5307, 6640, 7658, 4472, 300, 10577, 13150, 11917, 3131, 70, 4651, 16147, 14940, 3874, 9690, 6384, 6723, 7046, 8050, 3314, 15260, 9502, 10389, 1900, 14016, 2565, 4278, 3380, 14118, 4635, 1923, 7767, 2088, 2393, 531, 15552, 7239, 9835, 9072, 6194, 2694, 8545, 11594, 16235, 5560, 1308, 801, 13808, 4098, 3790, 1086, 2097, 11741, 8347, 12474, 14204, 12804, 360, 12142, 12172, 3502, 9350, 7625, 2478, 14695, 12481, 13465, 15341, 1237, 12006, 15266, 938, 12529, 4172, 16083, 5371, 9632, 9913, 14088, 13691, 15786, 15133, 4677, 15448, 985, 3903, 48, 6987, 11033, 14112, 9991, 7194, 7905, 8496, 5522, 6073, 1129, 8238, 9412, 15005, 15385, 4315, 8705, 208, 14763, 9451, 7234, 9899, 182, 9959, 8224, 8695, 5828, 12445, 15479, 16171, 56, 9821, 3057, 10409, 5080, 9442, 1551, 2525, 6553, 935, 1920, 9423, 8078, 7950, 11575, 3855, 16335, 6968, 4793, 1427, 37, 8889, 5208, 15128, 8877, 13025, 10800, 4862, 15727, 9426, 1292, 10519, 8304, 914, 810, 11206, 1470, 4839, 14495, 13113, 2851, 222, 1939, 13416, 14448, 5729, 13368, 6531, 5623, 2261, 4361, 5443, 12398, 4847, 6516, 2910, 5672, 6058, 15433, 1885, 3365, 13029, 258, 16108, 1834, 6274, 10230, 3896, 441, 16366, 5004, 14863, 3992, 9878, 12735, 13586, 12149, 15310, 14382, 9461, 16038, 11177, 12110, 6777, 11296, 806, 10338, 5687, 14870, 6206, 4072, 2846, 15137, 11065, 3683, 15628, 9889, 14126, 4062, 6715, 13783, 1143, 3087, 16272, 9050, 10045, 15848, 2217, 9149, 7637, 6442, 15225, 10165, 10947, 5202, 2925, 6572, 13841, 15502, 9506, 8081, 8994, 8917, 6911, 11797, 2249, 2333, 12571, 10465, 6409, 15064, 15648, 4868, 11047, 3573, 839, 14216, 1116, 14323, 4246, 11662, 14146, 15046, 8774, 7877, 6069, 7855, 16123, 13880, 7620, 972, 15110, 3412, 2255, 13241, 6844, 14427, 2034, 5227, 11420, 3347, 2807, 2189, 15022, 9548, 2179, 14983, 1785, 16181, 11988, 14609, 10235, 5406, 1400, 3579, 8984, 2730, 9622, 9394, 14003, 12093, 13738, 9776, 1849, 8336, 2528, 14503, 4562, 3218, 16013, 11446, 8381, 14105, 15147, 10769, 231, 14100, 15975, 9120, 2485, 12247, 13705, 5610, 13285, 6565, 3498, 6616, 273, 3754, 11318, 14805, 12666, 16062, 15714, 8061, 6620, 15746, 3891, 6992, 12742, 14303, 15382, 3388, 10227, 2843, 8320, 10139, 969, 6556, 1360, 3183, 12224, 15531, 11117, 9102, 5495, 10852, 9856, 5434, 15982, 612, 11099, 14157, 13096, 14857, 5344, 7256, 724, 7066, 660, 6945, 13044, 7859, 16097, 7783, 6559, 7649, 11391, 10295, 13985, 4768, 7743, 11996, 4623, 12356, 9831, 10765, 6289, 10155, 15280, 1554, 4879, 13717, 10342, 829, 3546, 8151, 10745, 10102, 13791, 13965, 12997, 7930, 162, 14346, 4535, 1894, 15930, 10348, 13338, 4927, 9980, 15764, 4442, 560, 14830, 1992, 11259, 13727, 8230, 3733, 11225, 10804, 7690, 15593, 10142, 14923, 3319, 13385, 8452, 12857, 3610, 4540, 15355, 14552, 14670, 12105, 9952, 11952, 10245, 11965, 1334, 6323, 1741, 13518, 7654, 2030, 456, 13978, 10458, 8605, 4681, 8323, 11923, 3251, 488, 12781, 9364, 2104, 10036, 6019, 7329, 11708, 13867, 4660, 13181, 9138, 2311, 5382, 11288, 265, 8117, 400, 3493, 2338, 14277, 3812, 14814, 6828, 9445, 10393, 8799, 15154, 3447, 1501, 10535, 7034, 7681, 12258, 9804, 3741, 14659, 8829, 3516, 13525, 11352, 13803, 128, 9321, 2600, 9315, 7846, 6007, 4513, 2884, 10669, 7296, 3911, 6302, 12434, 3066, 12413, 4005, 1174, 8145, 13760, 16338, 5161, 2753, 1525, 8957, 1322, 6181, 6293, 11482, 4466, 7597, 15402, 15671, 5075, 7561, 15814, 9228, 16134, 13892, 3463, 3661, 15373, 2162, 5693, 14890, 12615, 9262, 14306, 2736, 14027, 11129, 4738, 13678, 6233, 4972, 6507, 460, 15390, 10498, 6434, 11091, 5574, 7039, 14992, 2445, 11627, 2962, 4920, 9930, 6375, 6341, 12833, 3568, 8113, 16034, 5458, 2859, 408, 9528, 8779, 3639, 16127, 2003, 2276, 6422, 12488, 12745, 15103, 15637, 16259, 15720, 5141, 12929, 930, 12773, 5806, 2573, 8742, 7999, 8248, 5954, 9707, 6702, 9730, 9661, 16045, 3622, 1056, 7955, 12673, 277, 10489, 15965, 6743, 1491, 10506, 7731, 1859, 13358, 7144, 8490, 3858, 4823, 11375, 11907, 13374, 2952, 1613, 13403, 2111, 4294, 10435, 15774, 6298, 2921, 4376, 6455, 12028, 15569, 6822, 4508, 9392, 16011, 11660, 15108, 7781, 11097, 15744, 13283, 10763, 10743, 13383, 10243, 11706, 10456, 2882, 14657, 3055, 8236, 15784, 12170, 529, 8345, 649, 6382, 4070, 16364, 4866, 15223, 1549, 13023, 5621, 3894, 383, 2682, 9924, 5746, 11182, 10023, 14772, 6118, 7805, 14543, 2626, 7446, 11039, 1912, 1517, 1969, 11339, 7834, 10570, 11792, 10741, 1547, 5744, 5742, 4292, 12671, 7953, 15101, 9260, 11625, 8955, 5691, 2708, 2581, 4641, 10546, 1875, 7722, 13933, 1315, 7836, 4239, 14928, 1381, 6459, 12205, 6546, 2538, 1904, 11578, 3725, 3372, 7983, 15322, 14744, 2699, 719, 6696, 10446, 13272, 6497, 11341, 10085, 13006, 4275, 15338, 11794, 911, 826, 3444, 2840, 13735, 10186, 2863, 7427, 8748, 15319, 8952, 4002, 1856, 14548, 218, 5638, 15740, 6995, 15452, 9751, 10572, 9178, 11000, 7132, 12864, 2407, 4716, 15190, 2344, 12839, 6802, 11077, 14467, 1006, 15657, 9267, 14392, 1450, 12979, 13090, 8476, 5940, 13771, 5414, 2628, 6104, 9339, 2866, 12817, 4546, 4607, 6971, 15209, 8506, 897, 7448, 14259, 84, 14134, 12992, 10159, 6737, 14453, 97, 9025, 14591, 7807, 241, 7350, 11586, 15347, 13230, 8947, 12662, 11029, 13128, 15565, 14545, 15220, 4735, 15717, 10687, 8535, 14839, 8538, 11222, 13975, 13982, 13238, 14614, 14760, 5684, 255, 603, 6256, 5567, 1223, 5814, 7360, 5534, 11600, 1274, 14514, 3117, 434, 8374, 5546, 1971, 4686, 7457, 3978, 9355, 6893, 13655, 13884, 4854, 3404, 8064, 10906, 14852, 1519, 10690, 9197, 1650, 1820, 10838, 13954, 11267, 2285, 1914, 2375, 9038, 2829, 608, 16167, 14510, 9703, 13132, 8672, 9534, 15809, 3758, 11041, 8815, 1026, 13626, 4646, 2516, 7176, 12883, 10189, 11929, 15579, 14332, 4796, 14677, 5849, 11782, 16023, 22, 5657, 5292, 11726, 5065, 3487, 14412, 2715, 14842, 15731, 1486, 385, 15749, 1977, 8523, 8461, 4671, 1011, 3173, 12952, 7189, 5642, 2684, 8733, 1954, 12155, 13663, 3646, 7940, 15950, 11306, 15177, 10956, 14254, 1112, 9686, 237, 9926, 3717, 3396, 11280, 40, 7160, 14738, 14874, 7430, 8292, 11831, 5748, 553, 4628, 7367, 3263, 10701, 6887, 2802, 13121, 8568, 8039, 7439, 8180, 7204, 1430, 14020, 11870, 14754, 8751, 8125, 15170, 3188, 5616, 7014, 15090, 5332, 10025, 12536, 9560, 13996, 314, 15301, 1287, 12712, 4760, 12563, 4286, 4130, 4221, 11184, 9055, 14436, 6465, 4380, 13431, 10422, 14979, 8541, 14463, 15398, 989, 6623, 6120, 14974, 1246, 4092, 506, 10073, 10591, 1587, 9210, 9291, 4138, 495, 672, 14774, 12280, 6280, 15891, 1459, 5462, 5966, 3019, 12967, 3604, 1496, 12508, 10923, 12906, 6363, 10551, 10716, 9159, 15867, 1317, 11322, 3839, 14188, 9429, 12726, 9714, 3986, 4719, 5049, 5795, 9279, 12331, 13935, 16286, 8928, 5395, 11759, 13279, 7185, 1935, 15351, 295, 7505, 2634, 6261, 2236, 150, 14150, 9757, 1657, 7630, 950, 7008, 15862, 8810, 469, 14456, 7724, 8684, 11685, 13708, 4387, 12130, 16253, 6940, 5710, 9865, 7511, 4774, 8328, 1877, 6333, 8031, 13305, 9613, 8676, 3278, 6740, 11479, 10567, 6693, 5613, 14251, 12989, 4643, 15144, 14300, 7678, 11993, 8886, 10462, 2475, 9069, 10179, 15181, 10548, 323, 3820, 8580, 13421, 8665, 13836, 1122, 3045, 7972, 9920, 549, 9438, 10098, 11715, 1295, 8093, 1394, 15070, 2410, 13830, 15200, 7747, 326, 1162, 4042, 10961, 2710, 7309, 13496, 13632, 12620, 4980, 4394, 6627, 8283, 4355, 3541, 2583, 7115, 12700, 7382, 12311, 2134, 12690, 6028, 7228, 8426, 6854, 14034, 12207, 11358, 1639, 4338, 2021, 581, 6748, 11846, 3691, 6350, 3014, 6345, 12201, 6461, 6568, 3907, 7291, 122, 100, 6125, 9600, 12040, 5486, 6672, 13855, 11975, 10817, 1793, 11811, 7776, 1347, 3097, 14062, 9240, 6402, 7102, 15884, 15694, 15573, 104, 28, 16277, 2540, 13396, 1365, 4492, 14238, 15193, 15244, 12382, 7050, 8307, 306, 7991, 15620, 6548, 12016, 11471, 2384, 15184, 9188, 10620, 5972, 12361, 3049, 7838, 7168, 5630, 5102, 13168, 6797, 4350, 4197, 4210, 14951, 5763, 4241, 4601, 3010, 2400, 10182, 5962, 9457, 396, 2347, 6210, 175, 6591, 10522, 2593, 13555, 8009, 15456, 2638, 7399, 10129, 15662, 4503, 12369, 1074, 5770, 6048, 1566, 1560, 14635, 11512, 15924, 14930, 10658, 6223, 850, 568, 11879, 5026, 10732, 14647, 3953, 13288, 1383, 14010, 8893, 9028, 10966, 12440, 1507, 11364, 3374, 5923, 13600, 9088, 2743, 3336, 15667, 11073, 11590, 2175, 14969, 12196, 8279, 11487, 11694, 12633, 390, 8583, 11381, 1202, 14809, 3727, 16225, 7916, 16189, 1473, 6137, 12289, 10790, 7135, 8905, 8210, 10119, 16359, 5603, 735, 13451, 4152, 11580, 5648, 12922, 8019, 11549, 15083, 7814, 13136, 1773, 12267, 10631, 15050, 4990, 7882, 7965, 5174, 5018, 11201, 244, 14582, 15330, 1906, 12250, 200, 11310, 14374, 2268, 14746, 6788, 16074, 10540, 10597, 79, 4037, 10175, 14370, 4916, 7346, 3870, 14319, 8256, 7353, 3342, 5528, 2988, 2488, 2701, 6902, 481, 4415, 590, 15010, 8609, 7468, 5268, 12522, 7583, 9539, 12072, 5980, 11491, 993, 1197, 10484, 8846, 7985, 7697, 2817, 3245, 5109, 13344, 10972, 11209, 2791, 16350, 9943, 12867, 10009, 4450, 11166, 3823, 12000, 7567, 11327, 15324, 5517, 3586, 5251, 6698, 1270, 52, 15978, 7592, 1192, 3274, 7810, 7465, 7962, 780, 783, 6220, 5483, 7005, 8883, 15430, 6712, 7902, 6637, 5224, 721, 6016, 11256, 1584, 5062, 13235, 7454, 9525, 6504, 6379, 2404, 6199, 10913, 11003, 11457, 8412, 1948, 917, 8054, 3286, 9654, 13274, 15804, 2434, 7824, 13424, 14477, 14884, 9851, 15988, 3845, 6759, 9062, 14174, 13314, 12606, 15521, 6129, 12032, 3151, 10147, 1442, 10448, 7422, 6499, 1931, 2171, 12024, 8668, 6983, 16058, 4076, 9181, 15995, 2946, 11430, 813, 16067, 15832, 8268, 14285, 3971, 12115, 11343, 7976, 9013, 10605, 706, 9639, 5197, 14270, 978, 4400, 12274, 8195, 786, 7643, 15251, 7219, 12720, 2318, 10215, 1536, 9123, 7019, 14908, 10087, 14594, 5212, 10124, 3168, 6265, 6999, 370, 11816, 15642, 13960, 4781, 6241, 7546, 4957, 4808, 12758, 3429, 6681, 13008, 2667, 8778, 2002, 16258, 15636, 1055, 6701, 929, 5953, 4375, 15568, 2110, 13402, 10505, 276, 1858, 11906, 14991, 2961, 8112, 3567, 6433, 4971, 12614, 13677, 1524, 6180, 1173, 4004, 15813, 7596, 16133, 14889, 9923, 10022, 11038, 7445, 8954, 12670, 11338, 5741, 4865, 13022, 528, 12169, 15743, 16010, 10762, 14656, 3724, 15321, 6496, 13271, 6545, 4238, 2707, 1314, 7426, 8951, 825, 910, 9750, 217, 9177, 2343, 21, 11725, 1485, 15730, 7939, 8732, 8522, 5641, 13120, 7438, 4627, 552, 236, 15176, 3716, 7429, 671, 6279, 3603, 12966, 9209, 4091, 14978, 14973, 15089, 12535, 8750, 14753, 4285, 15300, 4220, 10421, 11266, 2374, 13131, 9702, 14676, 10188, 3757, 7175, 14851, 9196, 13654, 6892, 5533, 6255, 1273, 4685, 2865, 4606, 83, 14258, 5413, 12978, 12838, 14391, 13229, 11028, 14590, 9024, 14838, 15219, 11221, 254, 455, 8604, 9363, 12780, 14276, 264, 7328, 5381, 4512, 7295, 127, 13802, 3446, 6827, 10534, 8828, 3609, 14551, 1333, 11964, 3318, 10803, 4441, 3732, 4878, 828, 9830, 12355, 161, 10101, 4534, 15763, 1784, 14608, 9621, 2729, 230, 11445, 13737, 3217, 11419, 2188, 2254, 3411, 4245, 3572, 14145, 13879, 6619, 6991, 8319, 2842, 12665, 6615, 15974, 6564, 15981, 14156, 11116, 15530, 13043, 7255, 16096, 4767, 3158, 3702, 10576, 299, 1899, 8049, 69, 6722, 2096, 12473, 1307, 5559, 7766, 4277, 2392, 2693, 9898, 8223, 9820, 55, 207, 9411, 14111, 1128, 15340, 15265, 9349, 3501, 13690, 16082, 15132, 11032, 16271, 15847, 10946, 10164, 15647, 2332, 13840, 11796, 15627, 4061, 6205, 14869, 13585, 5003, 15309, 11295, 15127, 10799, 913, 8303, 1426, 11574, 9441, 8077, 6530, 4360, 221, 2850, 1884, 6515, 13028, 440, 2267, 16073, 4915, 14369, 5267, 4414, 8255, 6901, 7566, 5516, 12866, 9942, 1196, 9538, 8845, 10971, 10630, 7881, 15329, 14581, 7813, 5647, 8904, 4151, 11589, 12195, 13599, 5922, 14808, 12632, 16224, 7134, 11002, 1947, 2433, 15803, 1441, 15520, 14883, 13313, 13234, 6503, 5223, 6636, 3273, 1269, 7464, 8882, 3970, 7975, 977, 14269, 16066, 9180, 7421, 16057, 14907, 5211, 12719, 7218, 4780, 6998, 7545, 2666, 6853, 11357, 3690, 11845, 10816, 12039, 12200, 6124, 15619, 11470, 15243, 15192, 6401, 7775, 15883, 13395, 849, 5025, 8892, 14009, 15923, 6047, 15455, 1073, 6796, 4209, 3048, 12360, 9456, 4600, 2346, 8008, 8092, 2409, 10960, 4041, 12689, 7114, 13631, 3540, 3044, 548, 3819, 322, 12988, 11478, 15143, 9068, 12330, 8927, 294, 15350, 4718, 14187, 12905, 11321, 468, 8683, 1656, 9756, 7510, 12129, 8327, 3277, 10575, 8048, 7765, 5558, 15131, 15264, 9897, 1127, 220, 6514, 1425, 8302, 13839, 15846, 15626, 11294, 8318, 6614, 13042, 15529, 14144, 2187, 1783, 3216, 126, 6826, 14275, 12779, 4440, 14550, 4877, 15762, 11037, 12669, 15742, 12168, 9176, 8950, 3723, 1313, 1172, 7595, 6432, 3566, 928, 2001, 4374, 11905, 3602, 4090, 4284, 14752, 3715, 7437, 20, 5640, 13653, 6254, 14675, 9701, 12837, 4605, 13228, 253, 4914, 4413, 1195, 9941, 16223, 12194, 10629, 4150, 12718, 6997, 16065, 14268, 14882, 1946, 13233, 8881, 293, 14186, 7509, 9755, 15142, 547, 8091, 3539, 15242, 7774, 10815, 11844, 15454, 5024, 6795, 8007, 10626, 1998, 10627, 9753, 13651, 1999, 13040, 1125, 10814, 5023, 15141, 9754, 10628, 4412, 12717, 8880, 13041, 2186, 4439, 12778, 15625, 6513, 10574, 1126, 6431, 2000, 9175, 12167, 19, 4089, 13652, 252}; +constexpr uint16_t EXP_TABLE_14[] = {1, 7, 21, 107, 273, 1911, 5189, 11770, 389, 1179, 8129, 8038, 7187, 5208, 11689, 60, 180, 780, 2340, 16380, 16310, 15936, 15234, 8908, 11271, 1142, 7490, 4847, 15532, 14086, 1360, 6832, 1329, 7063, 708, 3164, 9620, 14479, 11247, 5102, 15275, 8723, 11802, 2597, 14075, 163, 873, 2079, 14429, 10705, 7508, 4749, 15746, 12492, 4646, 16083, 14459, 10531, 8074, 7831, 6596, 3453, 8819, 12090, 3525, 8539, 9954, 12493, 4641, 16070, 14352, 10290, 6397, 2770, 13374, 3320, 9960, 12539, 4771, 15688, 12986, 7524, 4637, 15986, 15132, 8470, 9985, 13668, 2686, 14202, 1060, 7420, 5845, 8202, 8277, 8648, 9499, 15138, 8620, 9255, 15510, 14240, 1570, 4846, 15531, 14099, 1339, 7073, 582, 4050, 12094, 3545, 8463, 10062, 13449, 4093, 12275, 4026, 11814, 2705, 13815, 2439, 15509, 14249, 1565, 4691, 16280, 16010, 14836, 11662, 201, 639, 3965, 11379, 1338, 7078, 595, 4025, 11823, 2734, 13642, 2740, 13580, 2918, 12338, 4316, 12853, 7881, 6238, 2491, 15393, 13477, 3897, 11695, 46, 202, 630, 3906, 11470, 1545, 4671, 16028, 14742, 11424, 1795, 5385, 11038, 4409, 14222, 1768, 4248, 13289, 7133, 818, 2462, 15578, 13892, 926, 2778, 13318, 3152, 9648, 14451, 10523, 7970, 7631, 4428, 14021, 25, 79, 493, 1411, 6281, 2974, 13018, 7236, 5629, 10706, 7517, 4786, 15679, 13311, 7103, 540, 3668, 11180, 4647, 16084, 14446, 10568, 7835, 6624, 3457, 8327, 9206, 11169, 4612, 15933, 15089, 9365, 16264, 16122, 14500, 11070, 4569, 13614, 2952, 12984, 7530, 4663, 16036, 14654, 12280, 3979, 11953, 2420, 15948, 15270, 8752, 12019, 2234, 15142, 8624, 9331, 15674, 13284, 7166, 987, 2817, 12551, 5975, 9348, 16383, 16319, 15999, 15167, 8703, 9630, 14521, 11117, 4192, 12545, 5957, 9466, 16005, 14809, 11597, 640, 3456, 8320, 9187, 11210, 4885, 14666, 11956, 2415, 15885, 14945, 10085, 13400, 3530, 8566, 9761, 12932, 7646, 4411, 14208, 1730, 4174, 12747, 5427, 11192, 4683, 16336, 16242, 15388, 13334, 3104, 9440, 16067, 14347, 10355, 6458, 3975, 11925, 2440, 15544, 14186, 1108, 7596, 4197, 12570, 5892, 9533, 15312, 9074, 10301, 6352, 2577, 13943, 775, 2325, 16235, 15443, 13819, 2467, 15465, 13661, 2769, 13367, 3271, 9813, 13256, 6970, 391, 1173, 8171, 8112, 7729, 6838, 1315, 7145, 958, 2618, 13990, 304, 1936, 5872, 8433, 8884, 11631, 622, 3850, 11574, 993, 2983, 12917, 7945, 7454, 4987, 14400, 10626, 7405, 5794, 8527, 9870, 12745, 5437, 11154, 4765, 15858, 12700, 5270, 12227, 3882, 11734, 321, 1735, 4181, 12682, 5364, 12013, 2272, 15008, 9506, 15245, 8929, 11460, 1599, 4797, 15634, 13116, 6646, 3555, 8617, 9276, 15575, 13927, 887, 2117, 14811, 11587, 682, 3414, 8866, 11533, 832, 2240, 14912, 10114, 14061, 193, 583, 4053, 12075, 3506, 8222, 8249, 8396, 8711, 11894, 2849, 12775, 5623, 10724, 7647, 4412, 14229, 1705, 4447, 14012, 374, 1602, 5070, 15179, 8371, 9082, 10245, 6264, 2377, 16127, 14527, 11135, 4126, 12411, 4387, 14280, 1850, 5542, 10323, 6618, 3367, 9205, 11176, 4667, 16000, 14786, 11532, 839, 2261, 14891, 9875, 12698, 5252, 12221, 3664, 11184, 4723, 16248, 15402, 13460, 4014, 11850, 2965, 13035, 7379, 5656, 8809, 12156, 3095, 9317, 15704, 13002, 7220, 5293, 12130, 3149, 9699, 14794, 11572, 1007, 2957, 12963, 7467, 5104, 15345, 9109, 10888, 5595, 10528, 8067, 7848, 6521, 3662, 11242, 5109, 15338, 9172, 11087, 4238, 13195, 6899, 1272, 7912, 6329, 2830, 12586, 6036, 9933, 12288, 4162, 12783, 5583, 10572, 7815, 6580, 3117, 9411, 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1416, 6328, 2825, 12607, 6143, 10204, 14199, 1031, 7189, 5194, 11735, 326, 1746, 4158, 12443, 4995, 15016, 9498, 15141, 8633, 9292, 15751, 12503, 4711, 16148, 15662, 13192, 6906, 1223, 7765, 7050, 663, 3557, 8635, 9282, 15789, 12289, 4165, 12794, 5540, 10333, 6640, 3569, 8663, 9542, 15025, 9557, 15048, 9274, 15557, 13849, 525, 3619, 10985, 5372, 11989, 2120, 14840, 11690, 53, 139, 945, 2583, 13925, 889, 2159, 14605, 12129, 3140, 9692, 14711, 11783, 2678, 14146, 1164, 8100, 7773, 7090, 575, 3773, 10547, 8186, 8135, 8052, 7277, 5410, 11215, 4878, 14603, 12147, 3130, 9382, 16145, 15669, 13257, 6973, 402, 1278, 7930, 6343, 2676, 14156, 1190, 8050, 7295, 5468, 10933, 5480, 10809, 5836, 8261, 8632, 9291, 15762, 12476, 4982, 14435, 10603, 7794, 7039, 92, 404, 1260, 7812, 6589, 3090, 9342, 15641, 13069, 6497, 3590, 10770, 5661, 8818, 12093, 3536, 8496, 10227, 14266, 1636, 4924, 14741, 11433, 1852, 5556, 10285, 6304, 2881, 12487, 4631, 15940, 15262, 8856, 11691, 50, 158, 986, 2822, 12562, 5948, 9621, 14472, 11258, 4997, 15034, 9572, 14943, 10207, 14206, 1080, 7336, 6009, 9294, 15753, 12541, 4785, 15670, 13248, 6914, 303, 1997, 5987, 9224, 15451, 13763, 2315, 16177, 15829, 12649, 5725, 9138, 10877, 5904, 9553, 15060, 9326, 15721, 12893, 8145, 7958, 7491, 4840, 15545, 14189, 1089, 7623, 4468, 13933, 833, 2247, 14933, 10217, 14332, 1974, 5634, 8751, 11950, 2345, 16351, 16223, 15583, 13919, 991, 2845, 12627, 5883, 8384, 8739, 11914, 2517, 15659, 13203, 6843, 1280, 6912, 289, 2023, 6069, 9770, 12981, 7497, 4830, 15419, 13539, 3819, 10385, 7060, 717, 3171, 9513, 15292, 8822, 12065, 3460, 8348, 9143, 10854, 5969, 9366, 16257, 16069, 14361, 10253, 6208, 2529, 15783, 12343, 4295, 12916, 7950, 7435, 4880, 14673, 12021, 2216, 15192, 8394, 8725, 11784, 2651, 14209, 1733, 4187, 12704, 5154, 11471, 1550, 4650, 16119, 14471, 11223, 4934, 14579, 10907, 5538, 10319, 6542, 3211, 10161, 13940, 782, 2346, 16342, 16224, 15458, 13676, 2630, 14290, 1916, 5236, 11629, 608, 3872, 11744, 451, 1353, 6911, 1244, 7700, 6733, 1986, 5966, 9419, 15890, 14908, 9974, 12449, 4901, 14810, 11588, 703, 3389, 9139, 10874, 5893, 9530, 15301, 8985, 10540, 8103, 7764, 7053, 642, 3470, 8362, 9013, 10728, 7675, 4544, 13665, 2661, 14139, 1507, 6569, 3198, 9594, 14853, 9817, 13292, 7110, 883, 2137, 14735, 11503, 1774, 4234, 13207, 6823, 1364, 6828, 1381, 6715, 1664, 4480, 13473, 3877, 11771, 386, 1166, 8106, 7799, 7012, 29, 83, 441, 1071, 7373, 5698, 9199, 11246, 5097, 15294, 8824, 12043, 3410, 8894, 11609, 748, 3204, 10140, 14007, 327, 1749, 4139, 12528, 4754, 15839, 12639, 5855, 8252, 8407, 8774, 12209, 3700, 11084, 4231, 13236, 6734, 1995, 6001, 9334, 15649, 13221, 6713, 1678, 4522, 13431, 3335, 8981, 10504, 8027, 7328, 5953, 9446, 16081, 14453, 10505, 8028, 7349, 5930, 9719, 14758, 11312, 1267, 7897, 6190, 2283, 14993, 9653, 14440, 10586, 7909, 6298, 3047, 13237, 6729, 2014, 5914, 9575, 14934, 10208, 14275, 1803, 5425, 11190, 4705, 16134, 15696, 13042, 7324, 6133, 10218, 14325, 1929, 5823, 8476, 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6030, 9867, 12754, 5500, 10837, 6088, 10073, 13548, 3782, 10322, 6621, 3378, 9118, 10937, 5452, 10949, 5176, 11401, 2012, 5908, 9549, 14976, 9666, 14637, 12161, 3812, 10428, 6999, 132, 924, 2772, 13356, 3206, 10130, 13981, 401, 1271, 7877, 6266, 2375, 16085, 14441, 10589, 7920, 6385, 2806, 13506, 3596, 10788, 5791, 8700, 9623, 14470, 11216, 4947, 14488, 11146, 4821, 15370, 13428, 3342, 9002, 10677, 7272, 5433, 11150, 4809, 15454, 13784, 2378, 16118, 14464, 11202, 4909, 14818, 11756, 487, 1461, 6155, 2064, 14448, 10514, 7965, 7538, 4735, 16220, 15574, 13920, 866, 2094, 14538, 10804, 5871, 8364, 8999, 10646, 7297, 6054, 9811, 13274, 6980, 253, 755, 3289, 9743, 12878, 8104, 7801, 6990, 203, 625, 3927, 11429, 1816, 5448, 10969, 5228, 11557, 920, 2760, 13432, 3370, 9174, 11073, 4260, 13149, 6353, 2582, 13922, 876, 2052, 14364, 10262, 6145, 2086, 14578, 10908, 5559, 10276, 6303, 3068, 13300, 7054, 651, 3505, 8215, 8198, 8305, 8500, 10223, 14318, 1992, 6008, 9289, 15772, 12438, 5024, 14913, 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12071, 3478, 8418, 8909, 11264, 1123, 7465, 5118, 15323, 9027, 10410, 6965, 426, 1110, 7586, 4175, 12748, 5414, 11219, 4954, 14503, 11063, 4582, 13715, 2235, 15137, 8613, 9240, 15403, 13459, 4027, 11809, 2692, 13724, 2198, 15330, 9196, 11239, 5078, 15107, 8523, 9874, 12701, 5265, 12246, 3905, 11463, 1590, 4738, 15791, 12303, 4207, 12588, 6022, 9907, 12666, 5668, 8925, 11376, 1331, 7065, 750, 3210, 10166, 13921, 869, 2107, 14497, 11045, 4504, 13545, 3805, 10259, 6170, 2151, 14645, 12233, 3868, 11604, 719, 3181, 9475, 15210, 8276, 8655, 9486, 15177, 8381, 9040, 10451, 6746, 1959, 5749, 9066, 10357, 6440, 4089, 12271, 4078, 12170, 3797, 10283, 6322, 2879, 12733, 5233, 11638, 545, 3815, 10421, 7016, 57, 175, 845, 2275, 15017, 9501, 15152, 8658, 9565, 15088, 9362, 16285, 16017, 14773, 11337, 1436, 6356, 2573, 13859, 683, 3409, 8887, 11622, 593, 4023, 11781, 2680, 14184, 1114, 7558, 4275, 13112, 6634, 3511, 8197, 8312, 8459, 10066, 13533, 3665, 11191, 4710, 16147, 15675, 13283, 7147, 944, 2576, 13936, 786, 2430, 15994, 15140, 8638, 9305, 15852, 12742, 5392, 11089, 4308, 12813, 7777, 6918, 307, 1945, 5839, 8268, 8583, 9462, 16033, 14629, 12217, 3660, 11236, 5087, 15164, 8694, 9633, 14340, 10334, 6649, 3534, 8554, 9845, 13096, 6554, 3303, 9909, 12648, 5722, 9127, 10774, 5633, 8742, 11921, 2452, 15596, 14022, 16, 112, 336, 1712, 4368, 14161, 1269, 7883, 6224, 2449, 15607, 13959, 471, 1317, 7163, 960, 2880, 12480, 4610, 15919, 14991, 9711, 14830, 11720, 283, 1857, 5319, 11892, 2863, 12749, 5409, 11206, 4913, 14774, 11328, 1443, 6249, 2366, 16314, 15972, 15230, 8248, 8395, 8722, 11805, 2608, 13968, 434, 1054, 7258, 5543, 10324, 6607, 3404, 8932, 11487, 1662, 4986, 14407, 10647, 7302, 6067, 9784, 13003, 7219, 5304, 12041, 3420, 8852, 11663, 206, 618, 3862, 11618, 589, 4067, 12201, 3644, 10932, 5487, 10796, 5799, 8532, 9935, 12302, 4200, 12601, 6125, 10146, 13837, 609, 3879, 11765, 424, 1112, 7560, 4249, 13294, 7112, 857, 2191, 15277, 8705, 11876, 2911, 12445, 5009, 15062, 9312, 15683, 12939, 7667, 4600, 13769, 2365, 16307, 15963, 15299, 8971, 10578, 7901, 6194, 2239, 15165, 8689, 9652, 14447, 10575, 7822, 6539, 3216, 10224, 14259, 1627, 4993, 15014, 9520, 15347, 9115, 10914, 5389, 11010, 4461, 13858, 684, 3396, 8924, 11383, 1318, 7154, 1023, 3069, 13299, 7067, 736, 3232, 10080, 13379, 3467, 8369, 9076, 10287, 6318, 2923, 12305, 4149, 12458, 4884, 14669, 11937, 2308, 16156, 15638, 13088, 6562, 3151, 9709, 14816, 11746, 461, 1379, 6697, 1790, 4346, 12999, 7191, 5188, 11773, 400, 1264, 7888, 6161, 2134, 14754, 11308, 1191, 8053, 7274, 5431, 11172, 4639, 15996, 15158, 8640, 9507, 15242, 8948, 11439, 1838, 5578, 10583, 7878, 6259, 2424, 15976, 15194, 8388, 8767, 11998, 2169, 14703, 11855, 2958, 12970, 7444, 4941, 14530, 10764, 5703, 9204, 11183, 4654, 16107, 14547, 10875, 5890, 9519, 15278, 8712, 11867, 3042, 13230, 6664, 1561, 4687, 16332, 16166, 15792, 12370, 4604, 13781, 2409, 15903, 14879, 9759, 12862, 7928, 6345, 2654, 14234, 1668, 4508, 13557, 3721, 10687, 7262, 5563, 10240, 6243, 2312, 16184, 15850, 12756, 5486, 10795, 5810, 8511, 10206, 14201, 1069, 7363, 5736, 9017, 10700, 7431, 4916, 14765, 11265, 1124, 7484, 5013, 15050, 9268, 15599, 14031, 47, 205, 611, 3881, 11743, 382, 1658, 4966, 14355, 10299, 6338, 2671, 14093, 1377, 6695, 1748, 4140, 12517, 4857, 15566, 13864, 666, 3526, 8530, 9949, 12400, 4370, 14175, 1247, 7709, 6770, 1919, 5245, 11602, 733, 3091, 9337, 15628, 13158, 6256, 2417, 15959, 15335, 9207, 11174, 4625, 15958, 15328, 9186, 11213, 4864, 14625, 12197, 3608, 10824, 6043, 9952, 12483, 4619, 15888, 14898, 9948, 12407, 4359, 14132, 1486, 6506, 3639, 10885, 5624, 10697, 7452, 4981, 14442, 10580, 7887, 6220, 2501, 15707, 12995, 7179, 5136, 11345, 1492, 6444, 4069, 12219, 3650, 11214, 4873, 14622, 12056, 3371, 9169, 11092, 4303, 12876, 8102, 7763, 7064, 745, 3231, 10205, 14192, 1042, 7294, 5467, 10912, 5379, 11048, 4539, 13312, 3138, 9678, 14601, 12157, 3088, 9328, 15667, 13275, 6979, 232, 664, 3528, 8568, 9739, 12882, 8188, 8149, 7946, 7447, 4932, 14589, 10929, 5492, 10861, 5984, 9217, 15460, 13694, 2616, 13992, 282, 1862, 5330, 11807, 2622, 14010, 356, 1596, 4788, 15661, 13185, 6853, 1146, 7526, 4627, 15960, 15306, 9012, 10735, 7662, 4523, 13424, 3346, 9086, 10265, 6188, 2277, 15035, 9571, 14922, 10164, 13935, 847, 2285, 14979, 9675, 14610, 12092, 3543, 8485, 10136, 13995, 275, 1913, 5231, 11564, 935, 2677, 14155, 1203, 7961, 7534, 4651, 16112, 14482, 11196, 4695, 16260, 16094, 14424, 10698, 7445, 4938, 14551, 10855, 5974, 9347, 16362, 16340, 16238, 15432, 13754, 2148, 14652, 12278, 4001, 11879, 2902, 12450, 4908, 14821, 11769, 396, 1188, 8060, 7253, 5514, 10391, 7046, 691, 3353, 9039, 10382, 7113, 862, 2202, 15302, 8976, 10515, 7962, 7527, 4628, 15949, 15265, 8741, 11928, 2475, 15441, 13813, 2441, 15551, 14207, 1087, 7357, 5906, 9567, 15102, 9400, 16203, 15539, 14171, 1219, 7753, 7134, 827, 2465, 15463, 13687, 2567, 13845, 553, 3807, 10269, 6192, 2225, 15127, 8487, 10134, 13953, 453, 1371, 6785, 1446, 6258, 2431, 15997, 15153, 8661, 9544, 15003, 9603, 14570, 10964, 5199, 11724, 263, 1813, 5483, 10800, 5875, 8440, 8843, 11730, 349, 1683, 4601, 13774, 2344, 16344, 16202, 15540, 14158, 1192, 8024, 7337, 6014, 9307, 15842, 12780, 5574, 10611, 7738, 6791, 1460, 6156, 2053, 14363, 10243, 6250, 2359, 16261, 16089, 14413, 10657, 7172, 5181, 11410, 1949, 5843, 8216, 8235, 8370, 9085, 10256, 6163, 2136, 14728, 11514, 1669, 4507, 13536, 3810, 10414, 6953, 510, 1530, 6630, 3475, 8441, 8844, 11719, 310, 1922, 5774, 8587, 9426, 15965, 15313, 9077, 10280, 6331, 2816, 12544, 5954, 9455, 16110, 14536, 10810, 5829, 8314, 8453, 10104, 13323, 3187, 9561, 15084, 9414, 15921, 15061, 9321, 15740, 12854, 7872, 6241, 2310, 16146, 15676, 13302, 7040, 673, 3431, 8757, 12008, 2299, 15073, 9445, 16088, 14410, 10676, 7279, 5420, 11237, 5080, 15145, 8605, 9392, 16243, 15387, 13315, 3147, 9713, 14772, 11342, 1417, 6335, 2844, 12628, 5870, 8363, 9010, 10749, 7568, 4305, 12822, 7712, 6849, 1126, 7474, 5055, 14876, 9750, 12801, 7749, 7162, 967, 2901, 12459, 4883, 14680, 11978, 2069, 14443, 10579, 7898, 6183, 2260, 14892, 9862, 12785, 5525, 10442, 6677, 1610, 5110, 15331, 9195, 11250, 5053, 14866, 9788, 13015, 7271, 5396, 11085, 4224, 13217, 6693, 1754, 4102, 12339, 4315, 12832, 7842, 6479, 3788, 10340, 6495, 3772, 10548, 8175, 8108, 7781, 6938, 359, 1589, 4747, 15760, 12466, 4956, 14517, 11081, 4252, 13301, 7049, 670, 3546, 8454, 10097, 13364, 3278, 9834, 13173, 6153, 2078, 14426, 10692, 7487, 5020, 15093, 9353, 16348, 16214, 15584, 14050, 236, 644, 3484, 8404, 8783, 12174, 3785, 10367, 6430, 3963, 11361, 1348, 6876, 1077, 7307, 6032, 9937, 12372, 4590, 13739, 2067, 14457, 10541, 8096, 7745, 7142, 915, 2809, 13551, 3791, 10349, 6496, 3585, 10759, 5750, 9059, 10314, 6549, 3274, 9846, 13089, 6565, 3162, 9606, 14577, 10901, 5512, 10393, 7084, 613, 3899, 11681, 4, 28, 84, 428, 1092, 7644, 4405, 14250, 1556, 4716, 16165, 15801, 12397, 4417, 14054, 240, 720, 3120, 9360, 16275, 16059, 14691, 11883, 2930, 12382, 4568, 13609, 2973, 13011, 7291, 5440, 10977, 5316, 11901, 2832, 12656, 5650, 8799, 12286, 3993, 11983, 2062, 14378, 10388, 7055, 652, 3492, 8316, 8471, 9990, 13681, 2581, 13931, 851, 2233, 15151, 8591, 9422, 15881, 14973, 10033, 13812, 2446, 15530, 14100, 1326, 7114, 855, 2213, 15227, 8227, 8330, 9173, 11080, 4251, 13280, 7138, 911, 2733, 13635, 2699, 13745, 2133, 14763, 11283, 1050, 7238, 5619, 10744, 7563, 4240, 13265, 7029, 106, 278, 1890, 5166, 11499, 1778, 4318, 12859, 7907, 6280, 2969, 13007, 7215, 5356, 11941, 2328, 16200, 15546, 14180, 1150, 7546, 4679, 16372, 16270, 16104, 14554, 10820, 6079, 9756, 12855, 7879, 6260, 2413, 15875, 14923, 10163, 13946, 804, 2556, 15860, 12686, 5352, 11961, 2380, 16100, 14590, 10936, 5451, 10960, 5203, 11672, 171, 849, 2231, 15109, 8537, 9964, 12519, 4855, 15588, 14078, 184, 808, 2520, 15624, 13178, 6180, 2269, 14867, 9787, 12994, 7180, 5125, 11322, 1221, 7771, 7072, 577, 4039, 12117, 3272, 9848, 13067, 6515, 3704, 11112, 4219, 12608, 5762, 8623, 9262, 15529, 14109, 1297, 7031, 100, 316, 1972, 5644, 8709, 11896, 2827, 12593, 6101, 9994, 13653, 2793, 13471, 3999, 11997, 2160, 14672, 12018, 2237, 15155, 8667, 9570, 14925, 10145, 13828, 606, 3994, 11974, 2097, 14487, 11175, 4630, 15939, 15243, 8947, 11450, 1861, 5339, 11808, 2691, 13705, 2301, 15091, 9371, 16290, 15916, 14982, 9680, 14675, 12027, 2178, 15246, 8936, 11515, 1666, 4494, 13451, 4083, 12249, 3948, 11268, 1151, 7549, 4690, 16287, 16031, 14751, 11423, 1982, 5690, 8839, 11766, 417, 1127, 7477, 5034, 14967, 9991, 13686, 2560, 13824, 578, 4046, 12138, 3189, 9547, 14994, 9660, 14423, 10727, 7638, 4355, 14120, 1434, 6342, 2675, 14169, 1229, 7779, 6920, 281, 1871, 5357, 11938, 2317, 16163, 15787, 12307, 4155, 12416, 5058, 15215, 8271, 8590, 9417, 15900, 14870, 9760, 12931, 7627, 4432, 13969, 437, 1035, 7217, 5302, 12067, 3466, 8374, 9057, 10308, 6591, 3100, 9300, 15823, 12591, 6031, 9868, 12743, 5399, 11076, 4287, 13084, 6422, 3907, 11465, 1564, 4692, 16269, 16097, 14565, 11001, 5260, 12165, 3832, 10472, 6907, 1216, 7744, 7137, 902, 2706, 13822, 2488, 15400, 13466, 3972, 11932, 2487, 15365, 13401, 3533, 8547, 9802, 13205, 6825, 1406, 6778, 1863, 5333, 11786, 2645, 14251, 1555, 4729, 16206, 15528, 14106, 1284, 6940, 373, 1611, 5105, 15350, 9088, 10979, 5322, 11863, 3014, 13138, 6396, 2773, 13355, 3219, 10233, 14220, 1766, 4274, 13119, 6655, 3548, 8468, 9999, 13646, 2728, 13656, 2762, 13430, 3328, 8960, 10595, 7754, 7127, 772, 2332, 16212, 15598, 14024, 58, 166, 882, 2142, 14746, 11396, 2047, 6141, 10194, 14173, 1233, 7735, 6820, 1373, 6803, 1496, 6408, 3865, 11599, 654, 3498, 8278, 8641, 9508, 15263, 8863, 11710, 89, 399, 1197, 8003, 7400, 5817, 8462, 10057, 13468, 3990, 12002, 2253, 14947, 10091, 13426, 3356, 9044, 10447, 6670, 1547, 4657, 16054, 14656, 11906, 2541, 15747, 12491, 4659, 16056, 14698, 11860, 3023, 13165, 6209, 2534, 15794, 12380, 4566, 13571, 2891, 12529, 4757, 15818, 12596, 6094, 10059, 13458, 4028, 11828, 2799, 13453, 4065, 12199, 3606, 10850, 5965, 9410, 15917, 14977, 9669, 14648, 12266, 4085, 12235, 3858, 11646, 537, 3663, 11245, 5088, 15233, 8901, 11320, 1227, 7793, 7030, 99, 297, 2015, 5917, 9586, 14909, 9969, 12468, 4942, 14539, 10803, 5882, 8391, 8758, 12001, 2244, 14940, 10198, 14145, 1157, 8091, 7904, 6273, 2982, 12914, 7964, 7541, 4714, 16183, 15815, 12567, 5927, 9684, 14671, 11951, 2350, 16330, 16180, 15822, 12584, 6042, 9959, 12502, 4704, 16129, 15685, 12953, 7565, 4226, 13231, 6671, 1548, 4644, 16093, 14417, 10741, 7592, 4217, 12622, 5800, 8569, 9740, 12871, 8087, 7876, 6269, 2386, 16062, 14712, 11818, 2741, 13579, 2931, 12377, 4557, 13634, 2700, 13732, 2110, 14522, 11108, 4191, 12732, 5238, 11619, 586, 4086, 12226, 3885, 11715, 298, 2006, 5922, 9679, 14606, 12136, 3195, 9569, 14916, 10142, 14009, 365, 1539, 4617, 15902, 14872, 9738, 12885, 8169, 8126, 7707, 6752, 1793, 5383, 11060, 4591, 13740, 2054, 14354, 10300, 6359, 2564, 13852, 534, 3682, 11054, 4521, 13438, 3384, 9128, 10811, 5826, 8303, 8558, 9833, 13180, 6198, 2211, 15209, 8285, 8688, 9651, 14458, 10532, 8095, 7932, 6357, 2570, 13878, 704, 3136, 9664, 14627, 12203, 3634, 10910, 5561, 10254, 6217, 2526, 15642, 13060, 6494, 3771, 10529, 8068, 7869, 6418, 3935, 11421, 1968, 5648, 8785, 12244, 3919, 11501, 1760, 4256, 13121, 6277, 3002, 12838, 7856, 6449, 4022, 11778, 2669, 14083, 1355, 6897, 1270, 7874, 6255, 2348, 16324, 16158, 15640, 13066, 6516, 3693, 11011, 4458, 13879, 711, 3157, 9643, 14386, 10460, 6775, 1892, 5180, 11413, 1928, 5816, 8457, 10076, 13559, 3719, 10645, 7304, 6041, 9966, 12521, 4829, 15410, 13532, 3670, 11170, 4621, 15874, 14924, 10150, 13841, 565, 3723, 10673, 7284, 5485, 10786, 5773, 8578, 9453, 16096, 14562, 10988, 5351, 11924, 2447, 15533, 14081, 1349, 6875, 1056, 7392, 5761, 8614, 9233, 15380, 13358, 3208, 10168, 13899, 947, 2585, 13903, 943, 2637, 14307, 2027, 6033, 9942, 12353, 4485, 13498, 3940, 11324, 1239, 7717, 6874, 1063, 7413, 5866, 8375, 9062, 10321, 6612, 3341, 8995, 10634, 7381, 5642, 8727, 11782, 2673, 14167, 1255, 7861, 6442, 4087, 12229, 3896, 11688, 59, 161, 871, 2101, 14475, 11251, 5050, 14855, 9815, 13254, 6928, 337, 1719, 4357, 14138, 1508, 6588, 3093, 9323, 15730, 12828, 7702, 6723, 2024, 6040, 9961, 12540, 4790, 15651, 13227, 6675, 1624, 5000, 15001, 9613, 14528, 10754, 5741, 8994, 10637, 7360, 5729, 8966, 10609, 7732, 6829, 1378, 6702, 1771, 4241, 13270, 7008, 1}; +typedef Field Field14; + +// 15 bit field +typedef RecLinTrans StatTable15; +constexpr StatTable15 QRT_TABLE_15({0, 276, 278, 1064, 274, 4986, 1056, 28002, 258, 1850, 4954, 25696, 1120, 16384, 28130}); +constexpr uint16_t LOG_TABLE_15[] = {32767, 0, 1, 15, 2, 30, 16, 240, 3, 255, 31, 1023, 17, 15345, 241, 45, 4, 60, 256, 3840, 32, 480, 1024, 15360, 18, 20898, 15346, 270, 242, 1038, 46, 7775, 5, 7790, 61, 15585, 257, 26919, 3841, 1053, 33, 9120, 481, 20913, 1025, 285, 15361, 29558, 19, 1263, 20899, 75, 15347, 3855, 271, 20038, 243, 15375, 1039, 18061, 47, 28380, 7776, 495, 6, 510, 7791, 10455, 62, 2046, 15586, 28395, 258, 10194, 26920, 15390, 3842, 18076, 1054, 21138, 34, 30690, 9121, 1278, 482, 90, 20914, 21581, 1026, 20053, 286, 7432, 15362, 8015, 29559, 3870, 20, 31160, 1264, 7805, 20900, 15600, 76, 5052, 15348, 1068, 3856, 720, 272, 16151, 20039, 26934, 244, 29573, 15376, 9546, 1040, 11065, 18062, 300, 48, 4080, 28381, 9135, 7777, 20928, 496, 16368, 7, 16383, 511, 127, 7792, 20278, 10456, 20943, 63, 8191, 2047, 4095, 15587, 9150, 28396, 2533, 259, 5224, 10195, 29588, 26921, 9561, 15391, 1503, 3843, 315, 18077, 23120, 1055, 19462, 21139, 11080, 35, 18301, 30691, 31175, 9122, 7820, 1279, 5606, 483, 5067, 91, 24026, 20915, 4863, 21582, 15615, 1027, 26949, 20054, 28620, 287, 3476, 7433, 16166, 15363, 6777, 8016, 1083, 29560, 735, 3871, 26386, 21, 16502, 31161, 525, 1265, 10470, 7806, 19185, 20901, 28410, 15601, 12444, 77, 29798, 5053, 2061, 15349, 21153, 1069, 22195, 3857, 30543, 721, 18091, 273, 8798, 16152, 10209, 20040, 15405, 26935, 9360, 245, 3885, 29574, 21921, 15377, 23436, 9547, 8030, 1041, 15825, 11066, 20068, 18063, 7447, 301, 18755, 49, 24564, 4081, 30705, 28382, 1293, 9136, 13956, 7778, 21596, 20929, 27159, 497, 1905, 16369, 105, 8, 120, 16384, 16391, 512, 7680, 128, 1920, 7793, 30581, 20279, 21611, 10457, 27174, 20944, 639, 64, 960, 8192, 24579, 2048, 30720, 4096, 28673, 15588, 13971, 9151, 24642, 28397, 31290, 2534, 1308, 260, 10958, 5225, 3900, 10196, 21936, 29589, 31400, 26922, 8045, 9562, 28071, 15392, 13876, 1504, 23451, 3844, 18770, 316, 10143, 18078, 5292, 23121, 7462, 1056, 29704, 19463, 15840, 21140, 20083, 11081, 13563, 36, 9029, 18302, 16517, 30692, 540, 31176, 27942, 9123, 19200, 7821, 11305, 1280, 28220, 5607, 10485, 484, 2076, 5068, 2616, 92, 15550, 24027, 29813, 20916, 9786, 4864, 28425, 21583, 12459, 15616, 24953, 1028, 9375, 26950, 29848, 20055, 27299, 28621, 15420, 288, 6698, 3477, 8813, 7434, 10224, 16167, 4320, 15364, 4212, 6778, 21168, 8017, 22210, 1084, 14618, 29561, 18106, 736, 26099, 3872, 16608, 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16004, 8968, 29787, 7619, 31339, 10634, 12075, 2370, 29342, 30629, 9485, 419, 19977, 8737, 27098, 19401, 26325, 7841, 1254, 26020, 22783, 30217, 12308, 20622, 8616, 14421, 26510, 25070, 5684, 32440, 16690, 29074, 30074, 13807, 19174, 25251, 27525, 26061, 22023, 10288, 22930, 13139, 2419, 7573, 25292, 25473, 28847, 25024, 26015, 17179, 31150, 25029, 8290, 1601, 3703, 18613, 3335, 28893, 13447, 13366, 6924, 23516, 10556, 8610, 14838, 11703, 16491, 12267, 14176, 1723, 16882, 25519, 4546, 27279, 7660, 21801, 24445, 23416, 20258, 26899, 2026, 7785, 32762, 31155, 505, 18296, 16378, 3880, 16497, 10953, 115, 9370, 9024, 11090, 7667, 21056, 26396, 19118, 10444, 3501, 22599, 6153, 626, 27394, 9586, 1318, 20266, 11381, 13573, 26227, 30568, 24963, 23355, 24973, 15575, 17184, 18235, 22235, 24629, 17245, 8441, 22046, 2521, 12812, 30745, 4484, 31277, 5317, 22421, 14120, 2035, 26334, 30769, 14974, 28660, 5999, 5388, 14019, 8179, 29628, 24877, 16075, 947, 18225, 19109, 15636, 3831, 8295, 30024, 9722, 10130, 17327, 11709, 30429, 23108, 6368, 30831, 28971, 5279, 6614, 11759, 6948, 21127, 14280, 31699, 1466, 13550, 8480, 20753, 19309, 19450, 19835, 22696, 27004, 29691, 17235, 12670, 2656, 26909, 25034, 6178, 6332, 28058, 14999, 19411, 23911, 1491, 7127, 5975, 5896, 13863, 26747, 21208, 29286, 10183, 13684, 22848, 5871, 31387, 27670, 27799, 21465, 5212, 31948, 16728, 7897, 10945, 24619, 22590, 21603, 1015, 3708, 20383, 24168, 29835, 25406, 14182, 12023, 28608, 1135, 7334, 8502, 27286, 12361, 25822, 18825, 7421, 3217, 26660, 27774, 4307, 30145, 11464, 7050, 3464, 3257, 24790, 21286, 6685, 4474, 23277, 1748, 29548, 1606, 2131, 20601, 26086, 3541, 30390, 23728, 26374, 10659, 8155, 19742, 16595, 17306, 25385, 9199, 8004, 4267, 12946, 13659, 14605, 31884, 13724, 14320, 6765, 31832, 3055, 32477, 4199, 22411, 27385, 31665, 471, 3340, 2097, 20470, 2603, 24287, 12273, 24690, 24014, 11257, 10095, 7384, 15537, 23978, 22147, 23695, 21570, 24128, 23662, 10920, 24940, 19276, 29253, 27491, 4851, 17830, 2185, 6482, 9773, 12802, 31482, 12479, 9110, 18618, 11203, 25935, 11292, 13106, 11670, 6232, 5594, 22296, 16051, 11840, 28207, 19617, 32117, 14909, 30679, 7294, 3374, 21440, 27929, 15685, 18981, 24161, 18289, 10004, 26818, 4758, 9016, 2511, 617, 20936, 233, 13452, 1913, 26825, 24049, 16616, 16888, 7905, 21909, 28094, 4766, 20775, 24452, 15264, 353, 28315, 9535, 12762, 20504, 30806, 17592, 8344, 13254, 12835, 23424, 864, 32206, 17954, 10682, 14009, 6061, 25690, 18051, 28898, 4145, 29143, 2273, 22517, 7088, 1356, 18743, 12739, 8417, 1185, 14671, 20193, 32053, 31515, 11054, 21530, 32169, 6589, 18380, 12873, 2759, 17510, 15813, 13033, 17675, 4931, 11602, 24867, 26218, 14101, 7766, 6929, 2637, 14890, 31646, 18806, 1729, 6515, 27147, 16814, 22763, 31551, 14082, 28296, 25671, 2582, 16357, 31625, 16986, 3806, 10421, 28586, 21887, 19668, 1893, 23203, 5450, 11183, 20363, 18215, 30004, 9806, 28370, 13371, 19688, 29929, 12123, 15738, 28019, 8949, 13944, 13788, 17160, 12198, 21365, 29473, 3142, 31570, 4069, 22107, 28770, 9697, 2979, 10368, 27723, 5517, 24552, 3992, 10775, 15256, 21048, 937, 23346, 27166, 15337, 10561, 5089, 10011, 17007, 14771, 4552, 25572, 22183, 25178, 21723, 15457, 21808, 31077, 23750, 2218, 709, 18578, 9881, 12645, 29390, 2841, 15036, 15775, 30531, 23828, 25786, 22482, 14736, 14964, 24252, 28445, 20028, 23521, 23223, 2913, 24725, 15192, 5832, 25156, 9348, 13231, 31253, 4650, 18880, 11530, 17377, 6534, 16140, 28167, 24321, 19810, 30917, 8877, 32584, 17863, 8786, 30338, 18527, 9254, 10852, 5378, 11372, 4884, 20889, 14843, 5470, 4390, 8242, 19763, 25525, 6435, 12432, 20554, 7003, 4437, 19071, 1419, 23864, 16833, 5041, 4718, 28722, 13525, 6130, 16003, 26612, 31338, 29786, 29341, 12074, 19976, 9484, 26324, 27097, 22782, 1253, 8615, 12307, 5683, 26509, 30073, 16689, 27524, 19173, 22929, 22022, 25291, 2418, 26014, 28846, 8289, 31149, 3334, 3702, 6923, 13446, 14837, 10555, 14175, 16490, 4545, 16881, 24444, 7659, 2025, 20257, 504, 32761, 16496, 16377, 9023, 114, 26395, 7666, 22598, 10443, 9585, 625, 13572, 20265, 23354, 30567, 18234, 15574, 8440, 24628, 30744, 2520, 22420, 31276, 30768, 2034, 5387, 28659, 24876, 8178, 19108, 946, 30023, 3830, 11708, 10129, 30830, 23107, 11758, 5278, 31698, 21126, 20752, 13549, 22695, 19449, 12669, 29690, 6177, 26908, 19410, 28057, 5974, 1490, 21207, 13862, 22847, 10182, 27798, 31386, 16727, 5211, 22589, 10944, 20382, 1014, 14181, 29834, 7333, 28607, 25821, 27285, 26659, 7420, 11463, 4306, 24789, 3463, 23276, 6684, 2130, 29547, 30389, 26085, 8154, 26373, 25384, 16594, 12945, 8003, 13723, 14604, 3054, 6764, 27384, 4198, 2096, 470, 12272, 2602, 10094, 24013, 22146, 15536, 23661, 21569, 29252, 24939, 2184, 4850, 31481, 9772, 11202, 9109, 11669, 11291, 16050, 5593, 32116, 28206, 3373, 30678, 18980, 27928, 26817, 18288, 616, 9015, 1912, 232, 16887, 24048, 4765, 21908, 352, 24451, 20503, 9534, 13253, 17591, 32205, 23423, 6060, 10681, 4144, 18050, 7087, 2272, 8416, 18742, 32052, 14670, 32168, 11053, 2758, 18379, 17674, 15812, 26217, 11601, 2636, 7765, 1728, 31645, 22762, 27146, 25670, 14081, 16985, 16356, 21886, 10420, 5449, 1892, 30003, 20362, 19687, 28369, 28018, 12122, 17159, 13943, 3141, 21364, 28769, 4068, 27722, 2978, 10774, 24551, 23345, 21047, 5088, 15336, 4551, 17006, 21722, 22182, 23749, 21807, 9880, 708, 15035, 29389, 25785, 30530, 24251, 14735, 23222, 20027, 5831, 24724, 31252, 9347, 17376, 18879, 24320, 16139, 32583, 30916, 18526, 8785, 11371, 10851, 5469, 20888, 25524, 8241, 7002, 12431, 23863, 19070, 28721, 5040, 26611, 6129, 12073, 29785, 27096, 9483, 12306, 1252, 16688, 26508, 22021, 19172, 28845, 2417, 3701, 31148, 10554, 13445, 16880, 16489, 20256, 7658, 16376, 32760, 7665, 113, 624, 10442, 30566, 20264, 24627, 15573, 31275, 2519, 28658, 2033, 945, 8177, 10128, 3829, 5277, 23106, 13548, 21125, 29689, 19448, 28056, 26907, 13861, 1489, 31385, 10181, 10943, 5210, 29833, 1013, 27284, 28606, 4305, 7419, 6683, 3462, 26084, 29546, 16593, 26372, 14603, 8002, 4197, 6763, 2601, 469, 15535, 24012, 24938, 21568, 9771, 4849, 11290, 9108, 28205, 5592, 27927, 30677, 9014, 18287, 24047, 231, 24450, 21907, 17590, 9533, 10680, 23422, 2271, 18049, 14669, 18741, 18378, 11052, 11600, 15811, 31644, 7764, 14080, 27145, 10419, 16355, 20361, 1891, 12121, 28368, 21363, 13942, 2977, 4067, 21046, 24550, 17005, 15335, 21806, 22181, 29388, 707, 14734, 30529, 24723, 20026, 18878, 9346, 30915, 16138, 10850, 8784, 8240, 20887, 19069, 12430, 6128, 5039, 9482, 29784, 26507, 1251, 2416, 19171, 13444, 31147, 7657, 16488, 112, 32759, 20263, 10441, 2518, 15572, 8176, 2032, 23105, 3828, 19447, 21124, 1488, 26906, 5209, 10180, 28605, 1012, 3461, 7418, 26371, 29545, 6762, 8001, 24011, 468, 4848, 21567, 5591, 9107, 18286, 30676, 21906, 230, 23421, 9532, 18740, 18048, 15810, 11051, 27144, 7763, 1890, 16354, 13941, 28367, 24549, 4066, 22180, 15334, 30528, 706, 9345, 20025, 8783, 16137, 12429, 20886, 29783, 5038, 19170, 1250, 16487, 31146, 10440, 32758, 2031, 15571, 21123, 3827, 10179, 26905, 7417, 1011, 8000, 29544, 21566, 467, 30675, 9106, 9531, 229, 11050, 18047, 16353, 7762, 4065, 28366, 705, 15333, 16136, 20024, 5037, 20885, 31145, 1249, 15570, 32757, 26904, 3826, 29543, 1010, 9105, 466, 18046, 228, 28365, 7761, 20023, 15332, 1248, 20884, 3825, 32756, 465, 1009, 7760, 227, 20883, 15331, 1008, 32755, 15330, 226, 225, 32754, 32752, 32753}; +constexpr uint16_t EXP_TABLE_15[] = {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 16387, 5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240, 20480, 8195, 16390, 15, 30, 60, 120, 240, 480, 960, 1920, 3840, 7680, 15360, 30720, 28675, 24581, 16393, 17, 34, 68, 136, 272, 544, 1088, 2176, 4352, 8704, 17408, 2051, 4102, 8204, 16408, 51, 102, 204, 408, 816, 1632, 3264, 6528, 13056, 26112, 19459, 6149, 12298, 24596, 16427, 85, 170, 340, 680, 1360, 2720, 5440, 10880, 21760, 10755, 21510, 10255, 20510, 8255, 16510, 255, 510, 1020, 2040, 4080, 8160, 16320, 32640, 32515, 32261, 31753, 30737, 28705, 24641, 16513, 257, 514, 1028, 2056, 4112, 8224, 16448, 131, 262, 524, 1048, 2096, 4192, 8384, 16768, 771, 1542, 3084, 6168, 12336, 24672, 16579, 389, 778, 1556, 3112, 6224, 12448, 24896, 17027, 1285, 2570, 5140, 10280, 20560, 8355, 16710, 655, 1310, 2620, 5240, 10480, 20960, 9155, 18310, 3855, 7710, 15420, 30840, 28915, 25061, 17353, 1937, 3874, 7748, 15496, 30992, 29219, 25669, 18569, 4369, 8738, 17476, 2187, 4374, 8748, 17496, 2227, 4454, 8908, 17816, 2867, 5734, 11468, 22936, 13107, 26214, 19663, 6557, 13114, 26228, 19691, 6613, 13226, 26452, 20139, 7509, 15018, 30036, 27307, 21845, 10921, 21842, 10919, 21838, 10911, 21822, 10879, 21758, 10751, 21502, 10239, 20478, 8191, 16382, 32764, 32763, 32757, 32745, 32721, 32673, 32577, 32385, 32001, 31233, 29697, 26625, 20481, 8193, 16386, 7, 14, 28, 56, 112, 224, 448, 896, 1792, 3584, 7168, 14336, 28672, 24579, 16389, 9, 18, 36, 72, 144, 288, 576, 1152, 2304, 4608, 9216, 18432, 4099, 8198, 16396, 27, 54, 108, 216, 432, 864, 1728, 3456, 6912, 13824, 27648, 22531, 12293, 24586, 16407, 45, 90, 180, 360, 720, 1440, 2880, 5760, 11520, 23040, 13315, 26630, 20495, 8221, 16442, 119, 238, 476, 952, 1904, 3808, 7616, 15232, 30464, 28163, 23557, 14345, 28690, 24615, 16461, 153, 306, 612, 1224, 2448, 4896, 9792, 19584, 6403, 12806, 25612, 18459, 4149, 8298, 16596, 427, 854, 1708, 3416, 6832, 13664, 27328, 21891, 11013, 22026, 11287, 22574, 12383, 24766, 16767, 765, 1530, 3060, 6120, 12240, 24480, 16195, 32390, 32015, 31261, 29753, 26737, 20705, 8641, 17282, 1799, 3598, 7196, 14392, 28784, 24803, 16837, 905, 1810, 3620, 7240, 14480, 28960, 25155, 17541, 2313, 4626, 9252, 18504, 4243, 8486, 16972, 1179, 2358, 4716, 9432, 18864, 4963, 9926, 19852, 6939, 13878, 27756, 22747, 12725, 25450, 18135, 3501, 7002, 14004, 28008, 23251, 13733, 27466, 22167, 11565, 23130, 13495, 26990, 21215, 9661, 19322, 5879, 11758, 23516, 14267, 28534, 24303, 15837, 31674, 30583, 28397, 24025, 15281, 30562, 28359, 23949, 15129, 30258, 27751, 22733, 12697, 25394, 18023, 3277, 6554, 13108, 26216, 19667, 6565, 13130, 26260, 19755, 6741, 13482, 26964, 21163, 9557, 19114, 5463, 10926, 21852, 10939, 21878, 10991, 21982, 11199, 22398, 12031, 24062, 15359, 30718, 28671, 24573, 16377, 32754, 32743, 32717, 32665, 32561, 32353, 31937, 31105, 29441, 26113, 19457, 6145, 12290, 24580, 16395, 21, 42, 84, 168, 336, 672, 1344, 2688, 5376, 10752, 21504, 10243, 20486, 8207, 16414, 63, 126, 252, 504, 1008, 2016, 4032, 8064, 16128, 32256, 31747, 30725, 28681, 24593, 16417, 65, 130, 260, 520, 1040, 2080, 4160, 8320, 16640, 515, 1030, 2060, 4120, 8240, 16480, 195, 390, 780, 1560, 3120, 6240, 12480, 24960, 17155, 1541, 3082, 6164, 12328, 24656, 16547, 325, 650, 1300, 2600, 5200, 10400, 20800, 8835, 17670, 2575, 5150, 10300, 20600, 8435, 16870, 975, 1950, 3900, 7800, 15600, 31200, 29635, 26501, 20233, 7697, 15394, 30788, 28811, 24853, 16937, 1105, 2210, 4420, 8840, 17680, 2595, 5190, 10380, 20760, 8755, 17510, 2255, 4510, 9020, 18040, 3315, 6630, 13260, 26520, 20275, 7781, 15562, 31124, 29483, 26197, 19625, 6481, 12962, 25924, 19083, 5397, 10794, 21588, 10411, 20822, 8879, 17758, 2751, 5502, 11004, 22008, 11251, 22502, 12239, 24478, 16191, 32382, 31999, 31229, 29689, 26609, 20449, 8129, 16258, 32516, 32267, 31765, 30761, 28753, 24737, 16705, 641, 1282, 2564, 5128, 10256, 20512, 8259, 16518, 271, 542, 1084, 2168, 4336, 8672, 17344, 1923, 3846, 7692, 15384, 30768, 28771, 24773, 16777, 785, 1570, 3140, 6280, 12560, 25120, 17475, 2181, 4362, 8724, 17448, 2131, 4262, 8524, 17048, 1331, 2662, 5324, 10648, 21296, 9827, 19654, 6543, 13086, 26172, 19579, 6389, 12778, 25556, 18347, 3925, 7850, 15700, 31400, 30035, 27301, 21833, 10897, 21794, 10823, 21646, 10527, 21054, 9343, 18686, 4607, 9214, 18428, 4091, 8182, 16364, 32728, 32691, 32613, 32457, 32145, 31521, 30273, 27777, 22785, 12801, 25602, 18439, 4109, 8218, 16436, 107, 214, 428, 856, 1712, 3424, 6848, 13696, 27392, 22019, 11269, 22538, 12311, 24622, 16479, 189, 378, 756, 1512, 3024, 6048, 12096, 24192, 15619, 31238, 29711, 26653, 20537, 8305, 16610, 455, 910, 1820, 3640, 7280, 14560, 29120, 25475, 18181, 3593, 7186, 14372, 28744, 24723, 16677, 585, 1170, 2340, 4680, 9360, 18720, 4675, 9350, 18700, 4635, 9270, 18540, 4315, 8630, 17260, 1755, 3510, 7020, 14040, 28080, 23395, 14021, 28042, 23319, 13869, 27738, 22711, 12653, 25306, 17847, 2925, 5850, 11700, 23400, 14035, 28070, 23375, 13981, 27962, 23159, 13549, 27098, 21431, 10093, 20186, 7607, 15214, 30428, 28091, 23413, 14057, 28114, 23463, 14157, 28314, 23863, 14957, 29914, 27063, 21357, 9945, 19890, 7015, 14030, 28060, 23355, 13941, 27882, 22999, 13229, 26458, 20151, 7533, 15066, 30132, 27499, 22229, 11689, 23378, 13991, 27982, 23199, 13629, 27258, 21751, 10733, 21466, 10167, 20334, 7903, 15806, 31612, 30459, 28149, 23529, 14289, 28578, 24391, 16013, 32026, 31287, 29805, 26841, 20913, 9057, 18114, 3463, 6926, 13852, 27704, 22643, 12517, 25034, 17303, 1837, 3674, 7348, 14696, 29392, 26019, 19269, 5769, 11538, 23076, 13387, 26774, 20783, 8797, 17594, 2423, 4846, 9692, 19384, 6003, 12006, 24012, 15259, 30518, 28271, 23773, 14777, 29554, 26343, 19917, 7065, 14130, 28260, 23755, 14741, 29482, 26199, 19629, 6489, 12978, 25956, 19147, 5525, 11050, 22100, 11435, 22870, 12975, 25950, 19135, 5501, 11002, 22004, 11243, 22486, 12207, 24414, 16063, 32126, 31487, 30205, 27641, 22513, 12257, 24514, 16263, 32526, 32287, 31805, 30841, 28913, 25057, 17345, 1921, 3842, 7684, 15368, 30736, 28707, 24645, 16521, 273, 546, 1092, 2184, 4368, 8736, 17472, 2179, 4358, 8716, 17432, 2099, 4198, 8396, 16792, 819, 1638, 3276, 6552, 13104, 26208, 19651, 6533, 13066, 26132, 19499, 6229, 12458, 24916, 17067, 1365, 2730, 5460, 10920, 21840, 10915, 21830, 10895, 21790, 10815, 21630, 10495, 20990, 9215, 18430, 4095, 8190, 16380, 32760, 32755, 32741, 32713, 32657, 32545, 32321, 31873, 30977, 29185, 25601, 18433, 4097, 8194, 16388, 11, 22, 44, 88, 176, 352, 704, 1408, 2816, 5632, 11264, 22528, 12291, 24582, 16399, 29, 58, 116, 232, 464, 928, 1856, 3712, 7424, 14848, 29696, 26627, 20485, 8201, 16402, 39, 78, 156, 312, 624, 1248, 2496, 4992, 9984, 19968, 7171, 14342, 28684, 24603, 16437, 105, 210, 420, 840, 1680, 3360, 6720, 13440, 26880, 20995, 9221, 18442, 4119, 8238, 16476, 187, 374, 748, 1496, 2992, 5984, 11968, 23936, 15107, 30214, 27663, 22557, 12345, 24690, 16615, 461, 922, 1844, 3688, 7376, 14752, 29504, 26243, 19717, 6665, 13330, 26660, 20555, 8341, 16682, 599, 1198, 2396, 4792, 9584, 19168, 5571, 11142, 22284, 11803, 23606, 14447, 28894, 25023, 17277, 1785, 3570, 7140, 14280, 28560, 24355, 15941, 31882, 30999, 29229, 25689, 18609, 4449, 8898, 17796, 2827, 5654, 11308, 22616, 12467, 24934, 17103, 1437, 2874, 5748, 11496, 22992, 13219, 26438, 20111, 7453, 14906, 29812, 26859, 20949, 9129, 18258, 3751, 7502, 15004, 30008, 27251, 21733, 10697, 21394, 10023, 20046, 7327, 14654, 29308, 25851, 18933, 5097, 10194, 20388, 8011, 16022, 32044, 31323, 29877, 26985, 21201, 9633, 19266, 5767, 11534, 23068, 13371, 26742, 20719, 8669, 17338, 1911, 3822, 7644, 15288, 30576, 28387, 24005, 15241, 30482, 28199, 23629, 14489, 28978, 25191, 17613, 2457, 4914, 9828, 19656, 6547, 13094, 26188, 19611, 6453, 12906, 25812, 18859, 4949, 9898, 19796, 6827, 13654, 27308, 21851, 10933, 21866, 10967, 21934, 11103, 22206, 11647, 23294, 13823, 27646, 22527, 12285, 24570, 16375, 32750, 32735, 32701, 32633, 32497, 32225, 31681, 30593, 28417, 24065, 15361, 30722, 28679, 24589, 16409, 49, 98, 196, 392, 784, 1568, 3136, 6272, 12544, 25088, 17411, 2053, 4106, 8212, 16424, 83, 166, 332, 664, 1328, 2656, 5312, 10624, 21248, 9731, 19462, 6159, 12318, 24636, 16507, 245, 490, 980, 1960, 3920, 7840, 15680, 31360, 29955, 27141, 21513, 10257, 20514, 8263, 16526, 287, 574, 1148, 2296, 4592, 9184, 18368, 3971, 7942, 15884, 31768, 30771, 28773, 24777, 16785, 801, 1602, 3204, 6408, 12816, 25632, 18499, 4229, 8458, 16916, 1067, 2134, 4268, 8536, 17072, 1379, 2758, 5516, 11032, 22064, 11363, 22726, 12687, 25374, 17983, 3197, 6394, 12788, 25576, 18387, 4005, 8010, 16020, 32040, 31315, 29861, 26953, 21137, 9505, 19010, 5255, 10510, 21020, 9275, 18550, 4335, 8670, 17340, 1915, 3830, 7660, 15320, 30640, 28515, 24261, 15753, 31506, 30247, 27725, 22681, 12593, 25186, 17607, 2445, 4890, 9780, 19560, 6355, 12710, 25420, 18075, 3381, 6762, 13524, 27048, 21331, 9893, 19786, 6807, 13614, 27228, 21691, 10613, 21226, 9687, 19374, 5983, 11966, 23932, 15099, 30198, 27631, 22493, 12217, 24434, 16103, 32206, 31647, 30525, 28281, 23793, 14817, 29634, 26503, 20237, 7705, 15410, 30820, 28875, 24981, 17193, 1617, 3234, 6468, 12936, 25872, 18979, 5189, 10378, 20756, 8747, 17494, 2223, 4446, 8892, 17784, 2803, 5606, 11212, 22424, 12083, 24166, 15567, 31134, 29503, 26237, 19705, 6641, 13282, 26564, 20363, 7957, 15914, 31828, 30891, 29013, 25257, 17745, 2721, 5442, 10884, 21768, 10771, 21542, 10319, 20638, 8511, 17022, 1279, 2558, 5116, 10232, 20464, 8163, 16326, 32652, 32539, 32309, 31849, 30929, 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11704, 23408, 14051, 28102, 23439, 14109, 28218, 23671, 14573, 29146, 25527, 18285, 3801, 7602, 15204, 30408, 28051, 23333, 13897, 27794, 22823, 12877, 25754, 18743, 4717, 9434, 18868, 4971, 9942, 19884, 7003, 14006, 28012, 23259, 13749, 27498, 22231, 11693, 23386, 14007, 28014, 23263, 13757, 27514, 22263, 11757, 23514, 14263, 28526, 24287, 15805, 31610, 30455, 28141, 23513, 14257, 28514, 24263, 15757, 31514, 30263, 27757, 22745, 12721, 25442, 18119, 3469, 6938, 13876, 27752, 22739, 12709, 25418, 18071, 3373, 6746, 13492, 26984, 21203, 9637, 19274, 5783, 11566, 23132, 13499, 26998, 21231, 9693, 19386, 6007, 12014, 24028, 15291, 30582, 28399, 24029, 15289, 30578, 28391, 24013, 15257, 30514, 28263, 23757, 14745, 29490, 26215, 19661, 6553, 13106, 26212, 19659, 6549, 13098, 26196, 19627, 6485, 12970, 25940, 19115, 5461, 10922, 21844, 10923, 21846, 10927, 21854, 10943, 21886, 11007, 22014, 11263, 22526, 12287, 24574, 16383, 32766, 32767, 32765, 32761, 32753, 32737, 32705, 32641, 32513, 32257, 31745, 30721, 28673, 24577, 16385, 1}; +typedef Field Field15; + +// 16 bit field +typedef RecLinTrans StatTable16; +constexpr StatTable16 QRT_TABLE_16({1842, 29368, 29370, 32406, 29374, 30898, 32414, 36026, 29358, 64036, 30866, 22674, 32478, 48838, 35898, 0}); +constexpr uint16_t LOG_TABLE_16[] = {65535, 0, 59241, 1, 52947, 2, 59242, 3155, 46653, 3156, 59243, 2820, 52948, 45328, 62396, 3, 40359, 4, 62397, 48283, 52949, 6310, 62061, 45329, 46654, 30365, 39034, 3157, 56102, 2821, 59244, 56381, 34065, 56382, 59245, 48483, 56103, 46416, 41989, 2822, 46655, 821, 16, 30366, 55767, 3158, 39035, 18175, 40360, 5975, 24071, 5, 32740, 48284, 62398, 59115, 49808, 45330, 62062, 52983, 52950, 39903, 50087, 6311, 27771, 6312, 50088, 12999, 52951, 5640, 42189, 39904, 49809, 55163, 40122, 45331, 35695, 52984, 62063, 33520, 40361, 25121, 60062, 5976, 59257, 6, 24072, 59176, 49473, 59116, 62399, 57015, 32741, 59536, 11881, 48285, 34066, 32920, 65216, 56383, 17777, 48484, 59246, 28902, 26446, 2823, 41990, 9465, 56104, 49130, 52821, 46417, 43514, 18176, 39036, 31533, 55768, 48715, 46689, 3159, 46656, 51438, 33609, 822, 43793, 30367, 17, 48148, 21477, 48149, 18, 42217, 43794, 62270, 6705, 30368, 46657, 44779, 64881, 51439, 35895, 823, 33610, 33236, 43515, 12437, 48869, 18177, 33828, 31534, 39037, 9130, 29401, 3160, 46690, 36174, 55769, 56540, 27226, 48716, 34067, 56138, 18827, 32921, 53768, 56384, 65217, 18026, 52963, 28903, 59247, 14261, 17778, 51103, 52882, 48485, 43179, 46418, 52822, 43058, 56105, 10158, 50721, 49131, 26447, 28526, 53242, 2824, 5587, 9466, 41991, 18250, 27772, 17153, 26626, 6313, 58922, 13000, 50089, 28076, 11483, 39905, 42190, 60277, 52952, 21330, 22608, 5641, 20152, 33521, 62064, 41678, 35696, 53883, 3171, 52985, 49810, 59201, 42836, 55164, 46527, 45332, 40123, 3976, 37220, 48286, 11882, 33185, 32742, 11434, 25239, 59537, 49474, 51638, 42421, 59117, 40395, 57016, 62400, 29114, 40362, 1417, 45144, 25122, 27315, 5977, 60063, 1931, 37499, 59177, 24073, 49571, 59258, 57810, 41854, 7, 15183, 8, 41855, 52285, 59259, 31031, 35923, 57811, 37500, 20995, 55976, 59178, 411, 49572, 24074, 32776, 40363, 12620, 38485, 1418, 58587, 25123, 45145, 21211, 29601, 1932, 60064, 54186, 27316, 1586, 26942, 5978, 37221, 19696, 6143, 48287, 42575, 33186, 11883, 36075, 27534, 59538, 25240, 15191, 32743, 28605, 2836, 11435, 23107, 29115, 62401, 3641, 40396, 32057, 29880, 57017, 49475, 28199, 50246, 51639, 20932, 59118, 42422, 24755, 27773, 60730, 49844, 17154, 12533, 6314, 26627, 49236, 47474, 28077, 50090, 51870, 58923, 30194, 11732, 13001, 46669, 5642, 22609, 38908, 52953, 47227, 7967, 21331, 11484, 34688, 44809, 39906, 46588, 60278, 42191, 1013, 36885, 3977, 40124, 58495, 46528, 49619, 36764, 45333, 49811, 57558, 3864, 59202, 44427, 55165, 42837, 54593, 20153, 56850, 22232, 33522, 46948, 41679, 62065, 49983, 64828, 52986, 3172, 54632, 35697, 51303, 11956, 53884, 21478, 60170, 10859, 48150, 20332, 42218, 19, 27133, 52628, 30369, 6706, 4872, 43795, 13575, 21782, 62271, 5189, 33237, 33611, 62691, 35896, 55803, 53983, 824, 46658, 26209, 15036, 44780, 16314, 51440, 64882, 62861, 13858, 48717, 27227, 13835, 55770, 62331, 35384, 56541, 29402, 31439, 47589, 3161, 62412, 36175, 46691, 42723, 43516, 26093, 52907, 12438, 36542, 18178, 48870, 28276, 40233, 9131, 39038, 13113, 33829, 25837, 63217, 31535, 30926, 18251, 41992, 14562, 5588, 46149, 26891, 9467, 26448, 16154, 5140, 28527, 18945, 2825, 53243, 20498, 43180, 39129, 45344, 46419, 36127, 43059, 52823, 30976, 34101, 49132, 50722, 8795, 56106, 3947, 22820, 10159, 34068, 61935, 60658, 56139, 38850, 32922, 18828, 26746, 21021, 18027, 65218, 63503, 53769, 36675, 61172, 56385, 31205, 48486, 52883, 45685, 17779, 12908, 43277, 51104, 52964, 25818, 51516, 28904, 35560, 14262, 59248, 58318, 8889, 58319, 59249, 47219, 35561, 4733, 45991, 14263, 52965, 28508, 24737, 25819, 29629, 28905, 51517, 62356, 31206, 50855, 14701, 48487, 49682, 45686, 52884, 37333, 59652, 51105, 43278, 41781, 17780, 7131, 26482, 12909, 34069, 32713, 6326, 61936, 32191, 56140, 60659, 11326, 52293, 26747, 18829, 57038, 38851, 50638, 14917, 32923, 23307, 56386, 61173, 29647, 53770, 59835, 47892, 36676, 21022, 44833, 60827, 18028, 20648, 63504, 65219, 29164, 30927, 61996, 13402, 18252, 65384, 14563, 41993, 20308, 36281, 9468, 26892, 10671, 5589, 49961, 29781, 46150, 21240, 20499, 53244, 17813, 18946, 31231, 8897, 2826, 26449, 14457, 22311, 16155, 62077, 28528, 5141, 33294, 16813, 10160, 22821, 24485, 56107, 65058, 62882, 3948, 34102, 4121, 25763, 49133, 23586, 8796, 50723, 32535, 43181, 63432, 21905, 39130, 43952, 46420, 45345, 58808, 14638, 30977, 52824, 27941, 36128, 3524, 18461, 43060, 21479, 923, 54436, 60171, 43550, 48151, 10860, 9812, 6239, 27134, 20, 30749, 20333, 32269, 42942, 42219, 41180, 62272, 21783, 57983, 43796, 64524, 45576, 13576, 52629, 18297, 23900, 30370, 5438, 4873, 6707, 54793, 40375, 62862, 64883, 47531, 16315, 5929, 32614, 51441, 46659, 36340, 40933, 26210, 1673, 44781, 15037, 42139, 5190, 28923, 28394, 33238, 38515, 62692, 33612, 44037, 40294, 825, 53984, 14589, 35897, 58995, 60254, 55804, 30591, 31536, 63218, 8695, 33830, 5086, 52201, 25838, 40234, 43829, 43325, 9132, 30470, 13114, 39039, 7036, 43517, 62774, 51264, 26094, 63105, 12439, 52908, 4572, 38133, 28277, 48871, 8977, 36543, 15819, 48299, 18179, 13859, 52726, 50556, 48718, 15938, 13836, 27228, 8460, 40654, 56542, 35385, 49104, 55771, 12713, 43689, 62332, 58534, 42724, 46692, 60965, 62413, 42666, 48338, 36176, 29403, 43719, 45009, 31440, 5662, 3162, 47590, 23945, 15184, 36120, 53876, 9, 4565, 52286, 41856, 57202, 14038, 57812, 35924, 13313, 59260, 34353, 20839, 31032, 46334, 32777, 24075, 38197, 412, 59759, 64113, 49573, 37501, 46213, 7281, 20996, 15488, 59179, 55977, 22672, 64430, 5979, 26943, 27851, 27317, 34956, 56397, 1587, 29602, 41863, 49509, 1933, 47689, 54187, 60065, 31681, 40364, 33968, 19915, 12621, 8742, 1419, 38486, 51535, 10020, 21212, 45146, 23216, 58588, 21405, 56567, 25124, 7564, 24756, 42423, 54258, 20933, 9021, 7541, 59119, 49476, 55891, 56037, 28200, 29090, 51640, 50247, 12744, 23108, 17416, 25145, 29116, 41295, 3642, 62402, 58327, 56118, 57018, 29881, 24130, 40397, 11246, 36429, 32058, 37222, 16626, 19799, 19697, 46613, 48288, 6144, 59293, 30248, 36076, 11884, 54134, 42576, 8111, 21982, 33187, 33939, 11436, 2837, 31143, 32744, 21181, 6819, 28606, 27535, 50968, 19543, 59539, 56923, 15192, 25241, 26066, 24632, 53885, 11957, 37262, 35698, 25859, 8268, 51304, 64829, 45372, 39855, 52987, 20597, 54633, 3173, 48910, 20154, 31722, 9860, 56851, 64381, 33523, 22233, 22651, 12651, 49984, 62066, 65425, 46949, 4914, 14204, 41680, 36886, 11288, 32835, 3978, 39050, 58496, 40125, 48540, 29833, 45334, 36765, 35740, 46529, 36391, 24682, 49620, 27807, 54594, 42838, 38969, 44428, 62374, 2501, 55166, 49812, 53845, 63188, 57559, 16526, 59203, 3865, 47934, 27774, 39329, 55641, 60731, 54364, 17155, 49845, 25327, 32556, 49237, 26628, 7761, 12534, 31579, 20452, 6315, 14727, 13002, 11733, 59695, 58924, 5671, 57209, 30195, 47475, 55067, 30381, 28078, 54878, 51871, 50091, 51950, 24911, 1014, 42192, 35142, 46589, 12285, 39391, 60279, 11485, 19614, 6614, 34689, 36983, 39907, 44810, 36808, 46670, 31186, 19524, 5643, 45222, 38909, 22610, 15592, 29266, 21332, 7968, 26362, 52954, 35731, 52024, 47228, 2595, 47229, 52025, 31346, 52955, 31431, 40925, 35732, 29267, 21362, 63974, 21333, 39697, 26363, 7969, 6918, 46671, 27297, 22214, 31187, 18443, 5644, 19525, 29248, 23335, 15593, 22611, 52222, 45223, 507, 56062, 38910, 24912, 16268, 44561, 1015, 8407, 35143, 42193, 12243, 43388, 60280, 39392, 8907, 46590, 49415, 31039, 12286, 53358, 36809, 44811, 28992, 36984, 27397, 35487, 39908, 11486, 21070, 837, 19615, 20188, 34690, 6615, 23766, 27775, 1642, 26419, 39330, 32, 60732, 55642, 14515, 25897, 25328, 49846, 37911, 54365, 45878, 5032, 17156, 45999, 6316, 20453, 12139, 12535, 36350, 50744, 31580, 32557, 56762, 44344, 49238, 8623, 7762, 26629, 34594, 17013, 51951, 50092, 6528, 54879, 6095, 23353, 51872, 47476, 16990, 53541, 55068, 41598, 28079, 30382, 50480, 14728, 46563, 38539, 13003, 54533, 59696, 11734, 12978, 14354, 30196, 57210, 65486, 58925, 19748, 22870, 5672, 24633, 22254, 55702, 53886, 7108, 37263, 11958, 63325, 59090, 51305, 8269, 31394, 35699, 13545, 14014, 25860, 29987, 48911, 3174, 47259, 20598, 30288, 4377, 54634, 64830, 63257, 43667, 45373, 23487, 52988, 39856, 53923, 14946, 41681, 14205, 16730, 46950, 17081, 11519, 4915, 12652, 58337, 24937, 49985, 2603, 65426, 62067, 40003, 20155, 8027, 8163, 31723, 16017, 56852, 9861, 18996, 55783, 22652, 22234, 39976, 64382, 46745, 27000, 33524, 10519, 47935, 3866, 33483, 16527, 61420, 18191, 59204, 49813, 33003, 58764, 53846, 56588, 57560, 63189, 29364, 27808, 20846, 63362, 54595, 19469, 38970, 42839, 29843, 17292, 55167, 2502, 61898, 44429, 481, 26241, 62375, 36887, 37603, 57138, 11289, 15611, 3979, 32836, 25726, 37658, 48541, 40126, 58958, 39051, 53494, 52514, 58497, 8344, 49621, 24683, 38160, 46530, 61282, 21647, 36392, 29834, 311, 62765, 45335, 12167, 35741, 36766, 54327, 15185, 11950, 60164, 36121, 48142, 10, 53877, 21471, 37256, 57203, 41857, 56917, 4566, 54430, 3518, 52287, 65480, 31033, 20840, 7102, 59261, 52695, 24455, 34354, 14039, 47958, 25975, 57813, 36648, 13314, 35925, 10226, 34886, 22673, 55978, 3225, 15489, 34131, 51689, 59180, 37502, 33676, 58230, 46214, 39282, 20997, 7282, 59267, 46335, 45410, 12003, 32778, 17606, 38198, 24076, 42284, 64679, 49574, 64114, 15257, 413, 35763, 48499, 59760, 34081, 25125, 56568, 21537, 58589, 40431, 41237, 21406, 10021, 17717, 65170, 21213, 26320, 23217, 45147, 59360, 40365, 14271, 30046, 33969, 34639, 12622, 19916, 61348, 60914, 51536, 38487, 49304, 8743, 39763, 35845, 1420, 64431, 28125, 22629, 5980, 22100, 27852, 26944, 18095, 32221, 1588, 56398, 33415, 27318, 23653, 37743, 34957, 34000, 31682, 60066, 64591, 47690, 38994, 8295, 54188, 29603, 63285, 52701, 41864, 53960, 1934, 49510, 19309, 24297, 26067, 25242, 39830, 56924, 24461, 2401, 15193, 27536, 41924, 64327, 50969, 45907, 59540, 19544, 33807, 33940, 1123, 37535, 11437, 37031, 31144, 2838, 17484, 24176, 28607, 6820, 61767, 32745, 45037, 742, 21182, 37223, 50811, 56480, 16627, 44970, 19698, 19800, 65090, 56811, 59294, 6145, 47296, 46614, 47237, 63813, 48289, 31839, 33188, 21983, 39561, 42577, 29901, 2683, 8112, 30249, 7817, 9525, 36077, 42005, 54135, 11885, 40070, 7565, 55192, 46432, 24757, 44262, 54259, 42424, 20040, 9644, 59120, 7542, 16063, 20934, 62481, 2166, 9022, 34360, 12745, 50248, 47599, 29091, 13960, 42810, 51641, 49477, 48840, 6419, 55892, 37395, 28201, 56038, 27351, 52240, 32059, 36430, 7869, 40398, 58203, 54671, 11247, 56119, 36056, 36372, 57019, 42044, 24131, 29882, 28973, 23109, 22379, 37425, 17417, 38715, 29117, 25146, 53666, 64903, 58328, 62403, 42130, 41296, 61473, 17651, 3643, 8890, 36333, 29826, 58320, 47582, 47220, 59250, 14254, 63806, 14264, 45992, 39996, 35562, 57748, 50908, 4734, 7744, 62357, 51518, 55874, 29630, 49944, 7019, 28906, 52966, 5623, 28059, 28509, 14545, 25820, 24738, 60713, 40040, 12910, 26483, 35579, 17781, 28874, 31903, 7132, 59653, 61650, 53465, 51106, 57819, 41782, 43279, 15967, 31207, 1536, 39919, 50856, 987, 48488, 14702, 27720, 9194, 37334, 52885, 52774, 49683, 36005, 16378, 45687, 58136, 29165, 65220, 22531, 20649, 53138, 21557, 63505, 21023, 31934, 28662, 44834, 50103, 18029, 60828, 34747, 23308, 63608, 35569, 56387, 43215, 29648, 61174, 60005, 41395, 36677, 47893, 61574, 53771, 57765, 25387, 59836, 34070, 57787, 27674, 32714, 13621, 61937, 6327, 31878, 2448, 11327, 60660, 43364, 32192, 50022, 45241, 56141, 3726, 32924, 14918, 54458, 38852, 40724, 16922, 50639, 52294, 25981, 15111, 26748, 50273, 57039, 18830, 50225, 1270, 43061, 18462, 53804, 36129, 58677, 47964, 3525, 14639, 2550, 2727, 30978, 1247, 27942, 52825, 37843, 43182, 19993, 49597, 63433, 49743, 39131, 21906, 22010, 22796, 58809, 45346, 4237, 43953, 4168, 6450, 46421, 16814, 4751, 11122, 10161, 18851, 24486, 22822, 47749, 35001, 3949, 62883, 50382, 56108, 57755, 52033, 65059, 49824, 32536, 50724, 15668, 23587, 2030, 17836, 8797, 34103, 42063, 4952, 4122, 30135, 49134, 25764, 49042, 30928, 5724, 10332, 61997, 13505, 18253, 13403, 63885, 40319, 20309, 41994, 13029, 65385, 50530, 52999, 14564, 23954, 46151, 29782, 14045, 5590, 52391, 47840, 49962, 36282, 11650, 1817, 9469, 15688, 10672, 26893, 50925, 27645, 33295, 5142, 33349, 62078, 24572, 24849, 28529, 26450, 47861, 14887, 14458, 525, 16156, 22312, 60630, 21241, 55025, 44674, 20500, 13249, 17814, 53245, 16767, 50629, 2827, 8898, 58078, 18947, 13690, 19772, 31232, 18338, 23946, 47591, 63354, 5663, 63097, 30968, 3163, 29404, 55440, 19565, 43720, 1974, 31441, 45010, 44178, 58535, 19243, 39078, 42725, 33561, 60966, 46693, 46239, 14303, 36177, 48339, 34186, 62414, 3072, 42616, 42667, 13860, 7351, 25428, 52727, 3566, 48719, 50557, 46009, 58087, 8461, 27229, 7459, 15939, 35931, 16357, 13837, 6357, 62333, 43690, 21845, 55772, 58046, 59131, 12714, 40655, 58400, 64155, 56543, 7910, 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50102, 31933, 28661, 39995, 63805, 57747, 50907, 14253, 47581, 36332, 29825, 55873, 7743, 49943, 7018, 60712, 14544, 5622, 28058, 52773, 9193, 36004, 16377, 27719, 986, 1535, 39918, 35578, 40039, 28873, 31902, 15966, 57818, 61649, 53464, 57037, 52292, 50637, 14916, 11325, 32190, 32712, 6325, 29646, 23306, 59834, 47891, 29163, 20647, 44832, 60826, 41780, 59651, 7130, 26481, 37332, 49681, 50854, 14700, 47218, 8888, 4732, 45990, 62355, 29628, 28507, 24736, 10670, 36280, 49960, 29780, 20307, 65383, 61995, 13401, 17812, 21239, 31230, 8896, 33293, 62076, 14456, 22310, 27940, 14637, 3523, 18460, 58807, 43951, 63431, 21904, 24484, 16812, 65057, 62881, 32534, 23585, 4120, 25762, 49103, 40653, 12712, 43688, 8459, 15937, 52725, 50555, 60964, 58533, 42665, 48337, 23944, 5661, 43718, 45008, 8976, 38132, 15818, 48298, 4571, 63104, 62773, 51263, 8694, 30590, 5085, 52200, 7035, 30469, 43828, 43324, 30748, 6238, 32268, 42941, 9811, 43549, 922, 54435, 57982, 41179, 64523, 45575, 54792, 5437, 18296, 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15190, 27533, 28604, 2835, 36074, 42574, 19695, 6142, 3640, 23106, 32056, 29879, 24754, 20931, 28198, 50245, 54185, 29600, 1585, 26941, 21210, 58586, 12619, 38484, 52284, 15182, 31030, 35922, 32775, 410, 20994, 55975, 51869, 47473, 30193, 11731, 49235, 12532, 60729, 49843, 38907, 46668, 47226, 7966, 1012, 46587, 34687, 44808, 54631, 64827, 51302, 11955, 49982, 46947, 56849, 22231, 58494, 36884, 49618, 36763, 54592, 44426, 57557, 3863, 63502, 21020, 36674, 61171, 26745, 38849, 61934, 60657, 45684, 31204, 12907, 43276, 58317, 35559, 25817, 51515, 8794, 34100, 3946, 22819, 30975, 36126, 39128, 45343, 14561, 30925, 46148, 26890, 20497, 18944, 16153, 5139, 4871, 52627, 13574, 21781, 27132, 20331, 60169, 10858, 62690, 5188, 55802, 53982, 62860, 16313, 26208, 15035, 13112, 40232, 25836, 63216, 28275, 36541, 26092, 52906, 13834, 13857, 62330, 35383, 42722, 62411, 31438, 47588, 14260, 52962, 51102, 52881, 18025, 53767, 56137, 18826, 43057, 43178, 10157, 50720, 18249, 5586, 28525, 53241, 36173, 29400, 56539, 27225, 9129, 33827, 12436, 48868, 42216, 21476, 62269, 6704, 33235, 35894, 44778, 64880, 60276, 11482, 21329, 22607, 28075, 58921, 17152, 26625, 41677, 20151, 53882, 3170, 3975, 46526, 59200, 42835, 49570, 37498, 57809, 41853, 1930, 27314, 1416, 45143, 33184, 37219, 11433, 25238, 29113, 40394, 51637, 42420, 9464, 26445, 49129, 52820, 28901, 17776, 32919, 65215, 31532, 43513, 48714, 46688, 48147, 43792, 51437, 33608, 57014, 49472, 59535, 11880, 59175, 59256, 25120, 60061, 12998, 27770, 5639, 42188, 33519, 35694, 55162, 40121, 2819, 46652, 45327, 62395, 3154, 52946, 65534, 59240, 48282, 40358, 6309, 62060, 56380, 56101, 30364, 39033, 52982, 49807, 39902, 50086, 59114, 32739, 5974, 24070, 48482, 34064, 46415, 41988, 18174, 55766, 820, 15}; +constexpr uint16_t EXP_TABLE_16[] = {1, 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535, 42, 126, 130, 390, 650, 1950, 2210, 6630, 10794, 32382, 33410, 34733, 35036, 39247, 44026, 64549, 1092, 3276, 5460, 16380, 16388, 49164, 16447, 49217, 16616, 49464, 17251, 50597, 20164, 54092, 30207, 40449, 41512, 58963, 10974, 32610, 33190, 33473, 34664, 35219, 39582, 44937, 61616, 4603, 12813, 22039, 64057, 3680, 4768, 14304, 22560, 59488, 14475, 18845, 55975, 28610, 45126, 53473, 28936, 37656, 46339, 57134, 24921, 41963, 58390, 11281, 29747, 40021, 42196, 60759, 14290, 22646, 59546, 14725, 19087, 57233, 24728, 41384, 58067, 10078, 27106, 47654, 52801, 21224, 63288, 6499, 11173, 31983, 34097, 36728, 37283, 45774, 55161, 31136, 35552, 40715, 41270, 58225, 9656, 28360, 45912, 54723, 32366, 33458, 34813, 34860, 39007, 43210, 63861, 2996, 7388, 9572, 28588, 45300, 53559, 29554, 38294, 48785, 50072, 17539, 52613, 22180, 64492, 3103, 5153, 15459, 17573, 52719, 22042, 64046, 3673, 4843, 14141, 22855, 60361, 15472, 17552, 52656, 22267, 64269, 3388, 5956, 14796, 19028, 57084, 25391, 42353, 61368, 12515, 20773, 62319, 5530, 16046, 17394, 50198, 19473, 54323, 31870, 33922, 36269, 38620, 47951, 52730, 22053, 64111, 3738, 5038, 13554, 23830, 59194, 10597, 31663, 36081, 38200, 48995, 49550, 17081, 51147, 18550, 55450, 27013, 47759, 53178, 20709, 61743, 4954, 13806, 24114, 57942, 9937, 27507, 48533, 50836, 19351, 56505, 26080, 44576, 62027, 5878, 15130, 19758, 55154, 31165, 35527, 40802, 41357, 58044, 10223, 26673, 47187, 51422, 22857, 60379, 15430, 17610, 52574, 22473, 63579, 2246, 6474, 11230, 31842, 33958, 36289, 38504, 47763, 53150, 20617, 61851, 4742, 14218, 22686, 59810, 15053, 20311, 53753, 29216, 38496, 47755, 53174, 20721, 61715, 4894, 13602, 24422, 57770, 8917, 26495, 43393, 64168, 4051, 4213, 12447, 20897, 62179, 5902, 14610, 19254, 56666, 26565, 43087, 63738, 2341, 7023, 11697, 30419, 39797, 44468, 63223, 6962, 11606, 30714, 38926, 43065, 63584, 2187, 6557, 10919, 32745, 32827, 32870, 32897, 33192, 33491, 34654, 35273, 39536, 44731, 62438, 5121, 15363, 17413, 52239, 21562, 64590, 1273, 3339, 5917, 14631, 19305, 56763, 26342, 43818, 64853, 2004, 2172, 6276, 10636, 31380, 36796, 37103, 45338, 54021, 29988, 40812, 41375, 57994, 10165, 26847, 47457, 52104, 23731, 58837, 11860, 29436, 38660, 47399, 52034, 24045, 58935, 10866, 32406, 33722, 34021, 36100, 38695, 47426, 52205, 23580, 58404, 11335, 29897, 40283, 42950, 59489, 14472, 18840, 55976, 28627, 45173, 53428, 29175, 37401, 46592, 55851, 28246, 45818, 55077, 31044, 35788, 40063, 42154, 60885, 13908, 23292, 61188, 12583, 21353, 62907, 7910, 9002, 25982, 44930, 61613, 4572, 12900, 22188, 64500, 3127, 5209, 15595, 17725, 53063, 20962, 61990, 5697, 15043, 20293, 53711, 29306, 38542, 48057, 52448, 21771, 65309, 268, 788, 1340, 3908, 4556, 12884, 22268, 64260, 3367, 5993, 14779, 19149, 57175, 25042, 41590, 59057, 11256, 31752, 33816, 35843, 37934, 48217, 50368, 19819, 55229, 30956, 35124, 39799, 44466, 63229, 6956, 11636, 30620, 39076, 43463, 64098, 3725, 5015, 13497, 24011, 58973, 10956, 32596, 33276, 33327, 34394, 35525, 40804, 41351, 58018, 10189, 26711, 47353, 51488, 23371, 60893, 13900, 23252, 61308, 12719, 21233, 63251, 6430, 11042, 32102, 34730, 35029, 39252, 43991, 64594, 1245, 3431, 6057, 14587, 18701, 56087, 27922, 46902, 55665, 27576, 48328, 50547, 20414, 53442, 29037, 37815, 46322, 56637, 26476, 43444, 64247, 3890, 4438, 13306, 21518, 64530, 1053, 3111, 5225, 15547, 17869, 52823, 21202, 63350, 6577, 10963, 32629, 33183, 33418, 34741, 35060, 39223, 43890, 64957, 1772, 2868, 7516, 10212, 26668, 47220, 51383, 23026, 59926, 15889, 16947, 50773, 19156, 57212, 25007, 41713, 59192, 10595, 31653, 36079, 38170, 48901, 49444, 17223, 50633, 20080, 53904, 30619, 39085, 43484, 64079, 3834, 4878, 13586, 24374, 57690, 9157, 25679, 44241, 62808, 8131, 8261, 24783, 41297, 58328, 9283, 27845, 46415, 57338, 24613, 41071, 57498, 8581, 25231, 42897, 59544, 14723, 19077, 57231, 24762, 41422, 57977, 9888, 27616, 48160, 50251, 19702, 54554, 32517, 33039, 33594, 34149, 36740, 37031, 45506, 53869, 30364, 39844, 44231, 62818, 8077, 8343, 25017, 41675, 59254, 10673, 31443, 36725, 37300, 45815, 55090, 31101, 35719, 40098, 42445, 61052, 12975, 22513, 63507, 2078, 6178, 10342, 30890, 35326, 39465, 44624, 62171, 5958, 14794, 19038, 57058, 25357, 42263, 61202, 12573, 21287, 62825, 8080, 8368, 25040, 41584, 59067, 11238, 31786, 33918, 36009, 38352, 48731, 49862, 18273, 51619, 23246, 61266, 12765, 21095, 63145, 7120, 11376, 29840, 40368, 42747, 60198, 15681, 18371, 51269, 22756, 59692, 15199, 19937, 54819, 31310, 36562, 37725, 46540, 56959, 25258, 43006, 59433, 14416, 18672, 55568, 27419, 48429, 51036, 18895, 55889, 28376, 45928, 54675, 32414, 33698, 33997, 36220, 38831, 47322, 51525, 23524, 60460, 13407, 23777, 58659, 12110, 29138, 37494, 46769, 56312, 27683, 46181, 56452, 26023, 44777, 62224, 5403, 16173, 16759, 50073, 17536, 52608, 22187, 64509, 3116, 5236, 15516, 17828, 52972, 21279, 62753, 8008, 8664, 25192, 42680, 60387, 15374, 17426, 52278, 21617, 64659, 1438, 3746, 5094, 13354, 23678, 58498, 11693, 30455, 39705, 44288, 63275, 6486, 11258, 31758, 33810, 35869, 37900, 48191, 50282, 19605, 54719, 32490, 33598, 34153, 36752, 37019, 45446, 53921, 30664, 39000, 43203, 63854, 2969, 7339, 9725, 28167, 45577, 54832, 31355, 36493, 37820, 46319, 56602, 26373, 43279, 64314, 3429, 6063, 14577, 18707, 56117, 28020, 47004, 55439, 27066, 47822, 53113, 20896, 62176, 5899, 14621, 19239, 56681, 26512, 43184, 63995, 2598, 7786, 8894, 26562, 43078, 63713, 2312, 6936, 11560, 30584, 39304, 43699, 65534, 41, 123, 141, 407, 697, 1995, 2141, 6375, 10537, 31611, 36237, 38588, 48111, 52250, 21509, 64527, 1082, 3150, 5330, 15734, 18330, 51374, 23001, 60011, 16022, 17338, 50382, 19833, 55179, 30902, 35290, 39493, 44772, 62215, 5410, 16230, 16810, 49918, 18217, 51579, 23462, 60650, 13589, 24383, 57665, 9192, 25656, 44104, 62707, 7486, 10050, 27078, 47690, 52981, 21300, 62812, 8143, 8273, 24819, 41237, 58132, 9495, 28473, 45387, 54262, 29745, 40019, 42206, 60745, 14320, 22544, 59440, 14459, 18573, 55703, 27282, 49078, 49393, 16696, 49992, 17907, 52757, 21012, 63036, 6767, 11953, 29651, 38005, 48308, 50679, 20018, 53846, 30417, 39795, 44478, 63209, 6928, 11568, 30544, 39408, 43579, 65126, 641, 1923, 2181, 6543, 10897, 32691, 32981, 33108, 33751, 33874, 36061, 38220, 49151, 49194, 16469, 49407, 16682, 50046, 17833, 52987, 21286, 62826, 8085, 8383, 25025, 41539, 59118, 11033, 32043, 34685, 35244, 39647, 44874, 61941, 4660, 13916, 23268, 61228, 12639, 21473, 62499, 7246, 9426, 28022, 47002, 55429, 27044, 47852, 53023, 20746, 62238, 5385, 16155, 16685, 50039, 17842, 52950, 21329, 62963, 7742, 8770, 26310, 43850, 65013, 1588, 2652, 7908, 9004, 25972, 44956, 61583, 4538, 13006, 22354, 63990, 2609, 7763, 8949, 26399, 43297, 64328, 3571, 5653, 14911, 20033, 53955, 30574, 39346, 43773, 65324, 351, 993, 1059, 3173, 5295, 15857, 17939, 51765, 24180, 58012, 10127, 26769, 47539, 51966, 24361, 57723, 9126, 25834, 44350, 63337, 6544, 10928, 32720, 32880, 32955, 33254, 33281, 34344, 35411, 40670, 41801, 58864, 11835, 29261, 38615, 47954, 52701, 22092, 64212, 3927, 4601, 12811, 22045, 64039, 3650, 4806, 14154, 23006, 60002, 16013, 17303, 50361, 19936, 54816, 31307, 36573, 37708, 46591, 56874, 25173, 42751, 60202, 15701, 18431, 51201, 22568, 59512, 14499, 18917, 55855, 28250, 45806, 55065, 30976, 35584, 40235, 42838, 59857, 14936, 20200, 54072, 30051, 40869, 41156, 57703, 9090, 25734, 44426, 63157, 7156, 11292, 29732, 40044, 42143, 60810, 14005, 23519, 60513, 13448, 23960, 59048, 11219, 31861, 33951, 36234, 38581, 48116, 52279, 21618, 64662, 1425, 3763, 5077, 13439, 23681, 58755, 11950, 29682, 37910, 48145, 50200, 19459, 54277, 31780, 33900, 35999, 38282, 48821, 50164, 17463, 52313, 21696, 64832, 2027, 2109, 6215, 10441, 31067, 35821, 39964, 41999, 60474, 13413, 23727, 58865, 11832, 29256, 38616, 47939, 52718, 22041, 64043, 3670, 4858, 14094, 22802, 60214, 15729, 18323, 51381, 23028, 59932, 15887, 16913, 50739, 19070, 56962, 25517, 42231, 60722, 14205, 22919, 60041, 16304, 16592, 49520, 17339, 50381, 19836, 55172, 30887, 35305, 39440, 44571, 61958, 5665, 14947, 20133, 54255, 29722, 39982, 42073, 60608, 13675, 24509, 57543, 8546, 25510, 42218, 60693, 14100, 22844, 60228, 15847, 17961, 51835, 24230, 58346, 9237, 27711, 46145, 56552, 25875, 44853, 61812, 5047, 13529, 23915, 59325, 10476, 31028, 35676, 40399, 42618, 60069, 16324, 16460, 49364, 16727, 50169, 17440, 52320, 21643, 64925, 1676, 2964, 7356, 9668, 28236, 45780, 55127, 31186, 35446, 40625, 41976, 58403, 11342, 29906, 40310, 42929, 59640, 14627, 19301, 56751, 26330, 43886, 64921, 1664, 2944, 7296, 9600, 28288, 45952, 54443, 32214, 34426, 35493, 40900, 41063, 57474, 8621, 25335, 42777, 59648, 15147, 19837, 55175, 30882, 35302, 39425, 44584, 62035, 5854, 15202, 19878, 55018, 31509, 36159, 38762, 47509, 51860, 24471, 57529, 8672, 25120, 42592, 60043, 16310, 16602, 49518, 17305, 50347, 19926, 54906, 31397, 36847, 36890, 45061, 53284, 28743, 37065, 45424, 54203, 29926, 40234, 42837, 59860, 14935, 20217, 54027, 30006, 40794, 41413, 57956, 9863, 27529, 48283, 50566, 20129, 54243, 29710, 39954, 42013, 60428, 13375, 23617, 58563, 11630, 30642, 39126, 43345, 64472, 3139, 5317, 15695, 18385, 51315, 22718, 59842, 14957, 20151, 54233, 29760, 40128, 42347, 61334, 12433, 20915, 62165, 5972, 14844, 18948, 56844, 25151, 42561, 60136, 16147, 16693, 50015, 17866, 52830, 21193, 63323, 6598, 10826, 32478, 33634, 34189, 36540, 37871, 46106, 56325, 25636, 44140, 62623, 7562, 9886, 27554, 48358, 50433, 20264, 53624, 29603, 38117, 48388, 50983, 18754, 56262, 27745, 46243, 56782, 26233, 43659, 65462, 241, 275, 821, 1375, 4065, 4131, 12389, 20655, 61937, 4664, 13896, 23256, 61288, 12691, 21173, 63455, 6218, 10462, 31074, 35750, 40129, 42344, 61331, 12446, 20898, 62182, 5889, 14595, 19205, 56591, 26426, 43342, 64505, 3104, 5216, 15520, 17888, 52768, 21067, 63197, 6988, 11732, 30332, 39556, 44967, 61634, 4461, 13239, 21721, 64875, 1942, 2234, 6606, 10834, 32502, 33562, 34053, 36644, 37191, 46050, 54285, 31804, 33860, 36071, 38146, 48941, 49500, 17359, 50257, 19672, 54632, 32659, 32949, 33268, 33335, 34418, 35517, 40940, 40991, 57354, 8245, 24671, 41185, 57608, 9011, 25941, 45055, 61482, 4181, 12543, 20737, 62211, 5422, 16242, 16790, 49850, 18405, 51247, 22618, 59630, 14617, 19243, 56701, 26540, 43252, 63799, 2930, 7574, 9914, 27598, 48210, 50397, 19788, 55252, 30807, 35065, 39200, 43851, 65014, 1585, 2643, 7925, 8991, 25889, 44899, 61838, 4793, 14283, 22621, 59623, 14594, 19206, 56586, 26421, 43359, 64458, 3189, 5279, 15777, 18147, 52005, 23876, 59340, 10367, 30849, 35203, 39598, 45017, 61504, 4331, 12605, 21319, 62921, 7792, 8848, 26544, 43216, 63835, 3014, 7242, 9438, 28002, 47014, 55489, 26984, 48056, 52451, 21774, 65298, 285, 807, 1385, 4027, 4301, 12631, 21497, 62475, 7222, 9306, 27886, 46386, 57213, 25004, 41716, 59191, 10610, 31638, 36026, 38373, 48644, 49703, 17986, 51910, 24417, 57763, 8910, 26450, 43510, 64049, 3704, 4744, 14232, 22696, 59896, 14883, 20069, 53935, 30682, 39022, 43161, 63872, 2731, 8189, 8199, 24585, 40987, 57350, 8225, 24675, 41125, 57796, 8807, 26281, 44027, 64550, 1089, 3267, 5445, 16335, 16465, 49395, 16702, 49986, 17901, 52791, 21106, 63126, 7057, 11443, 30165, 40575, 41642, 59349, 10324, 30972, 35076, 39719, 44354, 63469, 6172, 10276, 30828, 34996, 39415, 43570, 65149, 684, 2036, 2076, 6180, 10348, 30900, 35292, 39503, 44794, 62245, 5444, 16332, 16468, 49404, 16687, 50033, 17848, 52936, 21363, 62869, 7828, 9148, 25796, 44364, 63487, 6186, 10366, 30850, 35206, 39585, 45000, 61555, 4286, 12738, 21062, 63178, 7029, 11679, 30369, 39907, 44046, 62521, 7264, 9376, 28128, 46624, 55883, 28406, 45850, 54533, 32548, 33132, 33695, 33930, 36277, 38644, 47927, 52594, 22461, 63687, 2402, 7078, 11498, 30014, 40770, 41453, 57884, 9743, 27153, 48691, 49790, 18089, 52219, 23590, 58474, 11413, 30143, 40641, 41832, 58771, 11934, 29602, 38118, 48385, 50984, 18771, 56309, 27700, 46172, 56527, 25978, 44942, 61625, 4576, 12832, 22112, 64160, 4043, 4189, 12519, 20777, 62331, 5542, 16106, 17214, 50498, 20461, 53303, 28786, 37014, 45457, 53912, 30595, 39045, 43428, 64199, 3938, 4518, 13034, 22334, 63810, 3053, 7223, 9305, 27883, 46397, 57196, 24991, 41633, 59336, 10355, 30869, 35263, 39658, 44821, 61716, 4887, 13625, 24395, 57821, 8780, 26324, 43900, 64943, 1754, 2926, 7602, 9942, 27514, 48526, 50873, 19424, 56352, 25675, 44253, 62796, 8191, 8193, 24579, 40965, 57380, 8263, 24777, 41307, 58310, 9313, 27811, 46565, 56836, 25127, 42601, 60048, 16283, 16557, 49655, 16946, 50774, 19153, 57203, 25022, 41666, 59245, 10652, 31396, 36844, 36895, 45066, 53301, 28788, 37020, 45455, 53946, 30693, 38959, 43098, 63685, 2404, 7084, 11508, 29980, 40740, 41287, 58338, 9229, 27671, 46137, 56416, 25739, 44445, 63116, 7103, 11457, 30019, 40901, 41060, 57479, 8610, 25318, 42794, 59733, 15316, 19580, 54404, 32167, 34537, 35600, 40219, 42758, 59681, 15176, 19928, 54888, 31379, 36789, 37108, 45367, 54130, 30141, 40647, 41826, 58765, 11964, 29636, 37964, 48383, 50474, 20309, 53759, 29226, 38526, 47785, 53200, 20571, 61677, 4380, 13092, 21868, 65460, 247, 281, 811, 1405, 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1147, 3213, 5527, 16057, 17355, 50269, 19660, 54612, 32727, 32889, 32928, 33227, 33398, 34481, 35832, 39971, 42062, 60665, 13600, 24416, 57760, 8907, 26461, 43495, 64002, 3629, 4727, 13977, 23467, 60669, 13612, 24436, 57756, 8847, 26513, 43187, 63998, 2601, 7803, 8845, 26519, 43193, 63968, 2571, 7709, 8743, 26217, 43707, 65510, 1}; +typedef Field Field16; + +} + +Sketch* ConstructSmall(int bits, int implementation) +{ + switch (bits) { + case 2: return new SketchImpl(implementation); + case 3: return new SketchImpl(implementation); + case 4: return new SketchImpl(implementation); + case 5: return new SketchImpl(implementation); + case 6: return new SketchImpl(implementation); + case 7: return new SketchImpl(implementation); + case 8: return new SketchImpl(implementation); + case 9: return new SketchImpl(implementation); + case 10: return new SketchImpl(implementation); + case 11: return new SketchImpl(implementation); + case 12: return new SketchImpl(implementation); + case 13: return new SketchImpl(implementation); + case 14: return new SketchImpl(implementation); + case 15: return new SketchImpl(implementation); + case 16: return new SketchImpl(implementation); + default: return nullptr; + } +} + diff --git a/src/minisketch.cpp b/src/minisketch.cpp index 3c555cf..49b73ce 100644 --- a/src/minisketch.cpp +++ b/src/minisketch.cpp @@ -13,6 +13,8 @@ #include #endif +Sketch* ConstructSmall(int bits, int implementation); + Sketch* ConstructGeneric1Byte(int bits, int implementation); Sketch* ConstructGeneric2Bytes(int bits, int implementation); Sketch* ConstructGeneric3Bytes(int bits, int implementation); @@ -45,6 +47,7 @@ namespace { enum class FieldImpl { GENERIC = 0, + SMALL, #ifdef __x86_64__ CLMUL, CLMUL_TRI, @@ -75,6 +78,8 @@ Sketch* Construct(int bits, int impl) default: return nullptr; } + case FieldImpl::SMALL: + return ConstructSmall(bits, impl); #ifdef __x86_64__ case FieldImpl::CLMUL: case FieldImpl::CLMUL_TRI: { @@ -124,7 +129,7 @@ int minisketch_bits_supported(uint32_t bits) { } uint32_t minisketch_implementation_max() { - uint32_t ret = 0; + uint32_t ret = 1; #ifdef __x86_64__ ret += 2; #endif