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;
long long ax, ay, bx, by, cx, cy;
int main() {
  scanf("%lld%lld%lld%lld%lld%lld", &ax, &ay, &bx, &by, &cx, &cy);
  long long d0x = ax - bx, d0y = ay - by, d1x = ax - cx, d1y = ay - cy;
  if (d0x * d1y == d1x * d0y)
    puts("No");
  else {
    d1x = bx - cx, d1y = by - cy;
    if (d0x * d0x + d0y * d0y == d1x * d1x + d1y * d1y)
      puts("Yes");
    else
      puts("No");
  }
  return 0;
}