CodeForces 499C、Crazy Town_codeforces crazy town-优快云博客

本文介绍了一个基于平面几何的算法问题，即如何确定两点间需要穿越多少条直线才能从一点到达另一点。通过判断两点分别位于直线的哪一侧来确定是否需要穿越该直线。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

题目：

Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation a_ix + b_iy + c_i = 0, where a_i and b_i are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.

Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).

Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.

Input

The first line contains two space-separated integers x₁, y₁ ( - 10⁶ ≤ x₁, y₁ ≤ 10⁶) — the coordinates of your home.

The second line contains two integers separated by a space x₂, y₂ ( - 10⁶ ≤ x₂, y₂ ≤ 10⁶) — the coordinates of the university you are studying at.

The third line contains an integer n (1 ≤ n ≤ 300) — the number of roads in the city. The following n lines contain 3 space-separated integers ( - 10⁶ ≤ a_i, b_i, c_i ≤ 10⁶; |a_i| + |b_i| > 0) — the coefficients of the line a_ix + b_iy + c_i = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).

Output

Output the answer to the problem.

Example

Input

Output

Input

Output

Note

Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):

$\text{[math]}$ $\text{[math]}$

题意：给出两个点，求两个点之间有多少条直线，给出直线方程ax+by+c

思路：把一个点代入一条直线方程中，有3种结果：大于0，在这条直线上方；小于0，在这条直线下方；等于0 ，在直线上。如果两个点代入直线，一个大于0一个小于0，说明这条直线在两个点中间。故求两点之间有多少直线，只要一一代入直线方程就行

code：

#include<stdio.h>
typedef long long ll;
int main()
{
        ll x1,x2,y1,y2,a,b,c,n,l1,l2,num;
        while(~scanf("%lld%lld%lld%lld%lld",&x1,&y1,&x2,&y2,&n)){
                num=0;
                while(n--){
                        scanf("%lld%lld%lld",&a,&b,&c);
                        l1=a*x1+b*y1+c;
                        l2=a*x2+b*y2+c;
                        if((l1>0&&l2<0)||(l1<0&&l2>0)) num++;
                }
                printf("%lld\n",num);
        }
        return 0;
}