Problem: 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 <image>.

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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int maxn = 100000 + 10;
int main() {
  unsigned long long ax, ay, bx, by, cx, cy;
  while (
      ~scanf("%llu %llu %llu %llu %llu %llu", &ax, &ay, &bx, &by, &cx, &cy)) {
    unsigned long long ab = ((ax - bx) * (ax - bx) + (ay - by) * (ay - by));
    unsigned long long bc = ((bx - cx) * (bx - cx) + (by - cy) * (by - cy));
    if (!(ab == bc)) {
      printf("No\n");
      continue;
    }
    if (2 * bx == ax + cx && 2 * by == ay + cy)
      printf("No\n");
    else
      printf("Yes\n");
  }
  return 0;
}