E.cpp

#include <bits/stdc++.h>

#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 EACH(it,a) for(__typeof(a.begin()) it = a.begin(); it != a.end(); ++it)

#define DEBUG(x) { cout << #x << " = "; cout << (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
using namespace std;

#undef M_PI
const double M_PI = acos(-1.0);
#define EPS 1e-6

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

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

struct Point {
    double x, y;
    Point(double x = 0.0, double y = 0.0) : x(x), y(y) {}

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

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

    #define Comp(x) bool operator x (Point q) const { return cmp(q) x 0; }
    Comp(>) Comp(<) Comp(==) Comp(>=) Comp(<=) Comp(!=)
    #undef Comp

    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);
    }

    void read() {
        cin >> x >> y;
    }
};

int ccw(Point a, Point b, Point c) {
    return cmp((b-a)%(c-a),0);
}

double angle(Point a, Point o, Point b) { // angle AOB
    a = a - o; b = b - o;
    return acos((a * b) / sqrt(a.norm() * b.norm()));
}

// Distance from p to Line ab (closest Point --> c)
double distToLine(Point p, Point a, Point b, Point &c) {
    Point ap = p - a, ab = b - a;
    double u = (ap * ab) / ab.norm();
    c = a + (ab * u);
    return (p-c).len();
}

// Distance from p to segment ab (closest Point --> c)
double distToLineSegment(Point p, Point a, Point b, Point &c) {
    Point ap = p - a, ab = b - a;
    double u = (ap * ab) / ab.norm();
    if (u < 0.0) {
        c = Point(a.x, a.y);
        return (p - a).len();
    }
    if (u > 1.0) {
        c = Point(b.x, b.y);
        return (p - b).len();
    }
    return distToLine(p, a, b, c);
}

// NOTE: WILL NOT WORK WHEN a = b = 0.
struct Line {
    double a, b, c;
    Point A, B; // Added for polygon intersect line. Do not rely on assumption that these are valid

    Line(double a, double b, double c) : a(a), b(b), c(c) {} 

    Line(Point A, Point B) : A(A), B(B) {
        a = B.y - A.y;
        b = A.x - B.x;
        c = - (a * A.x + b * A.y);
    }
    Line(Point P, double m) {
        a = -m; b = 1;
        c = -((a * P.x) + (b * P.y));
    }
    double f(Point A) {
        return a*A.x + b*A.y + c;
    }
};

bool areParallel(Line l1, Line l2) {
    return cmp(l1.a*l2.b, l1.b*l2.a) == 0;
}

bool areSame(Line l1, Line l2) {
    return areParallel(l1 ,l2) && cmp(l1.c*l2.a, l2.c*l1.a) == 0
                && cmp(l1.c*l2.b, l1.b*l2.c) == 0;
}

bool areIntersect(Line l1, Line l2, Point &p) {
    if (areParallel(l1, l2)) return false;
    double dx = l1.b*l2.c - l2.b*l1.c;
    double dy = l1.c*l2.a - l2.c*l1.a;
    double d  = l1.a*l2.b - l2.a*l1.b;
    p = Point(dx/d, dy/d);
    return true;
}

void closestPoint(Line l, Point p, Point &ans) {
    if (fabs(l.b) < EPS) {
        ans.x = -(l.c) / l.a; ans.y = p.y;
        return;
    }
    if (fabs(l.a) < EPS) {
        ans.x = p.x; ans.y = -(l.c) / l.b;
        return;
    }
    Line perp(l.b, -l.a, - (l.b*p.x - l.a*p.y));
    areIntersect(l, perp, ans);
}

void reflectionPoint(Line l, Point p, Point &ans) {
    Point b;
    closestPoint(l, p, b);
    ans = p + (b - p) * 2;
}

bool order(Point A, Point B, Point C) {
    return min(A.x, C.x) <= B.x && B.x <= max(A.x, C.x)
            && min(A.y, C.y) <= B.y && B.y <= max(A.y, C.y);
}

bool intersect(Point A, Point B, Point X, Point Y) {
    if (ccw(A, B, X) == 0 && order(A, X, B)) return true;
    if (ccw(A, B, Y) == 0 && order(A, Y, B)) return true;

    if (ccw(X, Y, A) == 0 && order(X, A, Y)) return true;
    if (ccw(X, Y, B) == 0 && order(X, B, Y)) return true;

    if (ccw(A, B, X) * ccw(A, B, Y) < 0
            && ccw(X, Y, A) * ccw(X, Y, B) < 0)
        return true;
    return false;
}

int main() {
    Point A, B, M1, M2, W1, W2;
    while (cin >> A.x >> A.y) {
        B.read();
        W1.read(); W2.read();
        M1.read(); M2.read();

        Line W(W1, W2);
        Line M(M1, M2);

        Point A2, B2, AO, BO;
        reflectionPoint(M, A, A2);
        reflectionPoint(M, B, B2);

        areIntersect(Line(M1, M2), Line(A2, B), AO);
        areIntersect(Line(M1, M2), Line(B2, A), BO);


        if (!intersect(A, B, W1, W2) && !intersect(A, B, M1, M2)) cout << "YES";
        else if (!intersect(A, AO, W1, W2) && !intersect(AO, B, W1, W2) && intersect(A2, B, M1, M2)) cout << "YES";
        else if (!intersect(B, BO, W1, W2) && !intersect(BO, A, W1, W2) && intersect(B2, A, M1, M2)) cout << "YES";
        else cout << "NO";
        cout << endl;
    }
    return 0;
}