• norm()
  计算向量的模长
• db det(const pt &a, const pt &b)
  计算两个向量的叉积
• db dot(const pt &a, const pt &b)
  计算两个向量的点积
• db dist(const pt &a, const pt &b)
  计算两个点的距离
• pt rotate_point(const pt &p, db A)
  将向量 op 逆时针旋转 A （弧度）

#include <bits/stdc++.h>
#define nex(i) ((i+1)%n)
#define bef(i) ((i-1+n)%n)
#define INF 1000000000
using namespace std;
typedef double db;
const db eps = 1e-8;
const db pi = acos(-1.0);
inline db sqr(db x) {
    return x * x;
}
int gcd(int a, int b) {
    return b == 0 ? a : gcd(b, a % b);
}
int cmp(db x){
    return fabs(x) < eps ? 0 : (x > 0 ? 1 : -1);
}

namespace Point {
    struct pt {
        db x, y;
        pt() {}
        pt(db a, db b) : x(a), y(b) {}
        void input() {
            scanf("%lf%lf", &x, &y);
        }

        friend pt operator + (const pt &a, const pt &b) {
            return pt(a.x + b.x, a.y + b.y);
        }
        friend pt operator - (const pt &a, const pt &b) {
            return pt(a.x - b.x, a.y - b.y);
        }
        friend bool operator == (const pt &a, const pt &b) {
            return !cmp(a.x - b.x) && !cmp(a.y - b.y);
        }
        friend pt operator * (const pt &a, const db &b) {
            return pt(a.x * b, a.y * b);
        }
        friend pt operator * (const db &a, const pt &b) {
            return pt(a * b.x, a * b.y);
        }
        friend pt operator / (const pt &a, const db &b) {
            return pt(a.x / b, a.y / b);
        }
        friend bool operator < (const pt &a, const pt &b) {
            return cmp(a.x - b.x) < 0 || (cmp(a.x - b.x) == 0 && cmp(a.y - b.y) < 0);
        }
        double norm() {
            return sqrt(sqr(x) + sqr(y));
        }
    };
    db det(const pt &a, const pt &b) {
        return a.x * b.y - a.y * b.x;
    }
    db dot(const pt &a, const pt &b) {
        return a.x * b.x + a.y * b.y;
    }
    db dist(const pt &a, const pt &b) {
        return (a - b).norm();
    }
    pt rotate_point(const pt &p, db A) {
        db tx = p.x, ty = p.y;
        return pt(tx * cos(A) - ty * sin(A), tx * sin(A) + ty * cos(A));
    }
}
using namespace Point;