CF Round 432 B. Arpa and an exam about geometry

题目链接：http://codeforces.com/contest/851/problem/B

题目大意：纸上有三个点a, b, c，问有没有可能找到另一个点，将纸张绕着这个点选择一定角度后a与原来的b点重复，b与原来的c点重复。

解题思路：由于旋转相当于在画弧，因此可以发现另外找的点到a, b, c的距离都相等。又由于旋转的角度一样，因此只要保证a, b, c不在同一条线上并且a,b距离等于b, c距离即可。

可能需要注意精度问题。

代码：

const double eps = 1e-9;
const double PI = acos(-1);
ll powmod(ll a, ll b) { ll res = 1; a %= mod; assert(b >= 0); for (; b; b >>= 1) { if (b & 1)res = res*a%mod; a = a*a%mod; }return res; }
const int iadd[] = {0, 1, 0, -1}, jadd[] = {1, 0, -1, 0};
const int inf = 0x3f3f3f3f;
const int maxn = 1e6 + 5;
double ax, ay, bx, by, cx, cy;

void solve(){
    double tmp = (cx - bx) * (by - ay) - (bx - ax) * (cy - by);
    if(fabs(tmp) < eps){
        puts("No");
        return;
    }
    double d1 = (ax - bx) * (ax - bx) + (ay - by) * (ay - by);
    double d2 = (cx - bx) * (cx - bx) + (cy - by) * (cy - by);
    if(fabs(d1 - d2) < eps){
        puts("Yes");
        return;
    }
    puts("No");
}
int main(){
    scanf("%lf %lf %lf %lf %lf %lf", &ax, &ay, &bx, &by, &cx, &cy);
    solve();
}

题目：

B. Arpa and an exam about geometry

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Arpa is taking a geometry exam. Here is the last problem of the exam.

You are given three points a, b, c.

Find a point and an angle such that if we rotate the page around the point by the angle, the new position of a is the same as the old position of b, and the new position of b is the same as the old position of c.

Arpa is doubting if the problem has a solution or not (i.e. if there exists a point and an angle satisfying the condition). Help Arpa determine if the question has a solution or not.

Input

The only line contains six integers ax, ay, bx, by, cx, cy (|ax|, |ay|, |bx|, |by|, |cx|, |cy| ≤ 109). It's guaranteed that the points are distinct.

Output

Print "Yes" if the problem has a solution, "No" otherwise.

You can print each letter in any case (upper or lower).

Examples

input

0 1 1 1 1 0

output

Yes

input

1 1 0 0 1000 1000

output

No

Note

In the first sample test, rotate the page around (0.5, 0.5) by .

In the second sample test, you can't find any solution.