B3.cpp

#include <bits/stdc++.h>
#define int long long
#define FOR(i,a,b) for(int i=(a),_b=(b); i<=_b; ++i)
#define FORD(i,a,b) for(int i=(a),_b=(b); i>=_b; --i)
#define REP(i,a) for(int i=0,_a=(a); i < _a; ++i)

#define DEBUG(X) { cout << #X << " = " << (X) << endl; }
#define PR(A,n)  { cout << #A << " = "; FOR(_,1,n) cout << A[_] << ' '; cout << endl; }
#define PR0(A,n) { cout << #A << " = "; REP(_,n) cout << A[_] << ' '; cout << endl; }

#define sqr(x) ((x) * (x))
#define ll long long
#define __builtin_popcount __builtin_popcountll
#define SZ(x) ((int) (x).size())
using namespace std;

double safe_sqrt(double x) {
    return sqrt(max((double)0.0,x));
}
int GI(ll& x) {
    return scanf("%lld", &x);
}
#define EPS 1e-6
const double PI = acos(-1.0);

double DEG_to_RAD(double d) { return d * PI / 180.0; }
double RAD_to_DEG(double r) { return r * 180.0 / PI; }

inline int cmp(double a, double b) {
    return (a < b - EPS) ? -1 : ((a > b + EPS) ? 1 : 0);
}

struct Point { // <--> Vector
    double x, y;
    Point(double x = 0.0, double y = 0.0) : x(x), y(y) {}

    Point operator + (const Point& a) const { return Point(x+a.x, y+a.y); }
    Point operator - (const Point& a) const { return Point(x-a.x, y-a.y); }
    Point operator * (double k) const { return Point(x*k, y*k); }
    Point operator / (double k) const { return Point(x/k, y/k); }

    bool operator<(const Point &rhs) const { return make_pair(y,x) < make_pair(rhs.y,rhs.x); }
    bool operator==(const Point &rhs) const { return make_pair(y,x) == make_pair(rhs.y,rhs.x); }

    double operator * (const Point& a) const { return x*a.x + y*a.y; } // dot product
    double operator % (const Point& a) const { return x*a.y - y*a.x; } // cross product

    int cmp(Point q) const { if (int t = ::cmp(x,q.x)) return t; return ::cmp(y,q.y); }

    Point conj() { return Point(x, -y); }
    double norm() { return x*x + y*y; }

    // Note: There are 2 ways for implementing len():
    // 1. sqrt(norm()) --> fast, but inaccurate (produce some values that are of order X^2)
    // 2. hypot(x, y) --> slow, but much more accurate
    double len() { return sqrt(norm()); }

    Point rotate(double alpha) {
        double cosa = cos(alpha), sina = sin(alpha);
        return Point(x * cosa - y * sina, x * sina + y * cosa);
    }
};

int ccw(Point a, Point b, Point c) {
    return cmp((b-a)%(c-a),0);
}
typedef vector< Point > Polygon;

double area2(Point a, Point b, Point c) { return a%b + b%c + c%a; }
bool between(const Point &a, const Point &b, const Point &c) {
    return (fabs(area2(a,b,c)) < EPS && (a.x-b.x)*(c.x-b.x) <= 0 && (a.y-b.y)*(c.y-b.y) <= 0);
}

void ConvexHull(vector<Point> &pts) {
    sort(pts.begin(), pts.end());
    pts.erase(unique(pts.begin(), pts.end()), pts.end());
    vector<Point> up, dn;
    for (int i = 0; i < pts.size(); i++) {
        while (up.size() > 1 && area2(up[up.size()-2], up.back(), pts[i]) >= 0) up.pop_back();
        while (dn.size() > 1 && area2(dn[dn.size()-2], dn.back(), pts[i]) <= 0) dn.pop_back();
        up.push_back(pts[i]);
        dn.push_back(pts[i]);
    }
    pts = dn;
    for (int i = (int) up.size() - 2; i >= 1; i--) pts.push_back(up[i]);
    
    if (pts.size() <= 2) return;
    dn.clear();
    dn.push_back(pts[0]);
    dn.push_back(pts[1]);
    for (int i = 2; i < pts.size(); i++) {
        if (between(dn[dn.size()-2], dn[dn.size()-1], pts[i])) dn.pop_back();
        dn.push_back(pts[i]);
    }
    if (dn.size() >= 3 && between(dn.back(), dn[0], dn[1])) {
        dn[0] = dn.back();
        dn.pop_back();
    }
    pts = dn;
}
istream& operator >> (istream& cin, Point& p) {
    cin >> p.x >> p.y;
    return cin;
}
ostream& operator << (ostream& cout, Point& p) {
    cout << p.x << ' ' << p.y;
    return cout;
}
#define Det(a,b,c) ((double)(b.x-a.x)*(double)(c.y-a.y)-(double)(b.y-a.y)*(c.x-a.x))
bool in_convex(vector<Point>& l, Point p){
    int a = 1, b = l.size()-1, c;
    if (Det(l[0], l[a], l[b]) > 0) swap(a,b);
    // Allow on edge --> if (Det... > 0 || Det ... < 0)
    if (Det(l[0], l[a], p) >= 0 || Det(l[0], l[b], p) <= 0) return false;
    while(abs(a-b) > 1) {
        c = (a+b)/2;
        if (Det(l[0], l[c], p) > 0) b = c; else a = c;
    }
    // Alow on edge --> return Det... <= 0
    return Det(l[a], l[b], p) < 0;
}
Polygon cv123;
set< pair<int,int> > all123;

bool ok(int x, int y) {
    return all123.count(make_pair(x, y))
        || in_convex(cv123, Point(x, y));
}

bool check(int x, int y) {
    return ok(x, y) && ok(x+1, y) && ok(x, y+1) && ok(x+1, y+1);
}

#undef int
int main() {
#define int long long
    ios :: sync_with_stdio(0); cin.tie(0);
    cout << (fixed) << setprecision(9);
    int n, m;
    while (GI(n) == 1 && GI(m) == 1 && n && m) {
        // Generate magic polygon for checking 0 - 4
        all123.clear();
        cv123.clear();
        FOR(i,1,m) {
            int x, y; GI(x); GI(y);
            all123.insert(make_pair(x, y));
            cv123.push_back(Point(x, y));
        }
        ConvexHull(cv123);

        // Generate candidate points
        set< pair<int,int> > candidates;
        for(auto p : all123) {
            int x = p.first;
            int y = p.second;
            candidates.insert(make_pair(x, y));
            candidates.insert(make_pair(x, y-1));
            candidates.insert(make_pair(x-1, y));
            candidates.insert(make_pair(x-1, y-1));
        }

        // check candidate points
        Polygon all;
        for(auto p : candidates) {
            if (check(p.first, p.second)) all.push_back(Point(p.first, p.second));
        }
        ConvexHull(all);

        // print answer
        if (ccw(all[0], all[1], all[2]) > 0) reverse(all.begin(), all.end());

        vector< pair<int,int> > res;
        for(auto p : all) {
            res.push_back(make_pair(
                        (int) (round(p.x) + 1e-6),
                        (int) (round(p.y) + 1e-6)));
        }
        int start = 0;
        FOR(i,1,SZ(res)-1)
            if (res[i] < res[start]) start = i;

        cout << SZ(res) << '\n';
        REP(i,SZ(res)) {
            int u = (i + start) % SZ(res);
            cout << res[u].first << ' ' << res[u].second << '\n';
        }
    }
}