Little Petya likes to draw. He drew N red and M blue points on the plane in such a way that no three points lie on the same line. Now he wonders what is the number of distinct triangles with vertices in red points which do not contain any blue point inside.

Input

The first line contains two non-negative integer numbers N

Output

Output one integer — the number of distinct triangles with vertices in red points which do not contain any blue point inside.

Examples

4 1
0 0
10 0
10 10
5 4
2 1

2

5 5
5 10
6 1
8 6
-6 -7
7 -1
5 -1
10 -4
-10 -8
-10 5
-2 -8

7

向量法：這裏寫得很明了了：https://blog.csdn.net/v5zsq/article/details/79687164。。。（我還是太菜了

#include<bits/stdc++.h>
#define ll long long
#define rep(i,a,b) for(int i=a;i<=b;i++)
using namespace std;
const int maxn=510;
struct point{
    int x,y; point(){}
}a[maxn],b[maxn];
ll det(point O,point A,point B){
    return (1LL*A.x-O.x)*(B.y-O.y)-(1LL*B.x-O.x)*(A.y-O.y);
}
int dp[maxn][maxn];
int main()
{
    int N,M,ans=0; scanf("%d%d",&N,&M);
    a[0].x=-1e9-1; a[0].y=-1e9-1;
    rep(i,1,N) scanf("%d%d",&a[i].x,&a[i].y);
    rep(i,1,M) scanf("%d%d",&b[i].x,&b[i].y);
    rep(i,1,N) rep(j,1,N){
        if(i==j||det(a[0],a[i],a[j])<0) continue;
        rep(k,1,M)
         if(det(a[0],a[j],b[k])<=0&&det(a[j],a[i],b[k])<=0&&det(a[i],a[0],b[k])<=0)
          dp[i][j]++;
        dp[j][i]=-dp[i][j];
    }
    rep(i,1,N)
     rep(j,i+1,N)
      rep(k,j+1,N)
       ans+=(dp[i][j]+dp[j][k]+dp[k][i]==0);
    printf("%d\n",ans);
    return 0;
}

CodeForces - 13D ：Triangles（向量法：問多少個藍點三角形內部無紅點）