/*----------------------基础----------------------*/
const double pi = acos(-1);
const int maxp = 500;  //多边形最多点数
int equal(double a, double b)  //判断double相等
{
    if (fabs(a - b) <= 1e-8)
        return 1;
    else
        return 0;
}
int sign(double num)  //判断符号,负数返回-1,正数返回1,零返回0
{
    if (fabs(num) < 1e-8) return 0;
    if (num > 0) return 1;
    return -1;
}
int dcmp(double a, double b)  //浮点数比较,小于-1,等于0,大于1
{
    if (fabs(a - b) <= 1e-8) return 0;
    if (a < b) return -1;
    return 1;
}
/*---------------------------------------------------*/

/*----------------------点,向量----------------------*/
struct point
{
    double x, y;
    point(double x1 = 0, double y1 = 0) { x = x1, y = y1; }
    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 t) { return point(x * t, y * t); }
};
point rotate(point p, double theta)  //将点p旋转θ弧度
{
    return point(p.x * cos(theta) - p.y * sin(theta), p.x * sin(theta) + p.y * cos(theta));
}
double dot(point a, point b) { return a.x * b.x + a.y * b.y; }  //点乘
double cross(point a, point b) { return a.x * b.y - a.y * b.x; }  //叉乘
double len(point a) { return sqrt(dot(a, a)); }  //向量模长
double angle(point a, point b) { return dot(a, b) / len(a) / len(b); } //两向量夹角
/*---------------------------------------------------*/

/*----------------------直线,线段----------------------*/
struct line  //直线
{
    point s, v;
    line(point s1 = {0, 0}, point v1 = {1, 0}) { s = s1, v = v1; }
};
struct seg  //线段
{
    point u, v;
    seg(point u1 = {0, 0}, point v1 = {1, 0}) { u = u1, v = v1; }
};
double angle(line a)  //求直线与x轴夹角
{
    return atan2(a.v.y, a.v.x);
}
point intersection(line a, line b)  //求直线交点
{
    point u = a.s - b.s;
    double t = cross(b.v, u) / cross(a.v, b.v);
    return a.s + a.v * t;
}
/*---------------------------------------------------*/

/*----------------------多边形----------------------*/
struct polygon
{
    point p[maxp];
    int cnt;
    polygon() { cnt = 0; }
    void add(point pp) { p[cnt++] = pp; }  //加点
};
int stk[maxn];  //求凸包栈
bool used[maxn];  //求凸包标记已使用点
polygon andrew(polygon poly)  //求凸包
{
    int top = 0;
    sort(poly.p, poly.p + poly.cnt, [](point a, point b) {
        if (equal(a.x, b.x)) return a.y < b.y;
        return a.x < b.x;
    });
    stk[++top] = 0;
    used[0] = true;
    for (int i = 1; i < poly.cnt; i++)
    {
        while (top >= 2 && sign(cross(poly.p[stk[top]] - poly.p[stk[top - 1]], poly.p[i] - poly.p[stk[top]])) >= 0)
        {
            used[stk[top]] = false;
            top--;
        }
        stk[++top] = i;
        used[i] = true;
    }
    int tmp = top;
    used[0] = false;
    for (int i = poly.cnt - 1; i >= 0; i--)
    {
        if (used[i]) continue;
        while (top > tmp && sign(cross(poly.p[stk[top]] - poly.p[stk[top - 1]], poly.p[i] - poly.p[stk[top]])) >= 0)
        {
            used[stk[top]] = false;
            top--;
        }
        stk[++top] = i;
        used[i] = true;
    }
    polygon res;
    for (int i = 1; i <= top; i++) res.add(poly.p[stk[i]]);
    return res;
}
double area(polygon &poly)  //求多边形面积
{
    double res = 0;
    if (poly.cnt < 3) return 0;
    for (int i = 1; i < poly.cnt; i++)
    {
        res += cross(poly.p[i], poly.p[i - 1]);
    }
    res += cross(poly.p[0], poly.p[poly.cnt - 1]);
    return fabs(res / 2.0);
}
double len(polygon &poly)  //求多边形周长
{
    double res = 0;
    for (int i = 1; i < poly.cnt; i++)
    {
        res += len(poly.p[i] - poly.p[i - 1]);
    }
    res += len(poly.p[0] - poly.p[poly.cnt - 1]);
    return res;
}
int on_right(line a, line b, line c)  //判断bc交点是否在a的右边
{
    point o = intersection(b, c);
    if (sign(cross(o - a.s, a.v)) == 1) return 1;
    return 0;
}
int q[maxn];  //半平面交双端队列
polygon half_plane_intersection(polygon poly[], int cnt)  //求半平面交
{
    vector<line> li;
    for (int i = 0; i < cnt; i++)
    {
        for (int j = 1; j < poly[i].cnt; j++)
        {
            point s, v;
            s = poly[i].p[j - 1];
            v = poly[i].p[j] - poly[i].p[j - 1];
            li.push_back(line(s, v));
        }
        if (poly[i].p[0] != poly[i].p[poly[i].cnt - 1])
        {
            point s, v;
            s = poly[i].p[poly[i].cnt - 1];
            v = poly[i].p[0] - poly[i].p[poly[i].cnt - 1];
            li.push_back(line(s, v));
        }
    }
    sort(li.begin(), li.end(), [](line a, line b) {
        double num1, num2;
        num1 = atan2(a.v.y, a.v.x);
        num2 = atan2(b.v.y, b.v.x);
        if (equal(num1, num2)) return sign(cross(b.s - a.s, a.v)) == 1;
        return num1 < num2;
    });
    int hh = 0, tt = -1;
    for (int i = 0; i < li.size(); i++)
    {
        if (i > 0 && dcmp(angle(li[i]), angle(li[i - 1])) == 0) continue;
        while (hh + 1 <= tt && on_right(li[i], li[q[tt - 1]], li[q[tt]])) tt--;
        while (hh + 1 <= tt && on_right(li[i], li[q[hh]], li[q[hh + 1]])) hh++;
        q[++tt] = i;
    }
    while (hh + 1 <= tt && on_right(li[q[hh]], li[q[tt - 1]], li[q[tt]])) tt--;
    while (hh + 1 <= tt && on_right(li[q[tt]], li[q[hh]], li[q[hh + 1]])) hh++;
    q[++tt] = q[hh];
    int k = 0;
    polygon ans;
    for (int i = hh; i < tt; i++)
        ans.add(intersection(li[q[i]], li[q[i + 1]]));
    return ans;
}
/*---------------------------------------------------*/