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 double eps = 1e-9;
int double_cmp(double a) {
  if (fabs(a) < eps) return 0;
  return a > 0 ? 1 : -1;
}
int main() {
  double ax, ay, bx, by, cx, cy;
  while (scanf("%lf %lf %lf %lf %lf %lf", &ax, &ay, &bx, &by, &cx, &cy) !=
         EOF) {
    double midx = (ax + cx) / 2;
    double midy = (ay + cy) / 2;
    if (double_cmp(midx - bx) == 0 && double_cmp(midy - by) == 0) {
      puts("No");
      continue;
    }
    double up = (ay - cy) * (by - midy);
    double down = (ax - cx) * (bx - midx) * (-1);
    if (double_cmp(up - down) == 0)
      puts("Yes");
    else
      puts("No");
  }
  return 0;
}