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;
int const N = 1e6 + 1, oo = 2e9 + 1;
int n, m, q, k, x, y, a[N];
int ax, ay, bx, by, cx, cy;
long long dist(int x1, int y1, int x2, int y2) {
  return (1ll * (x1 - x2) * (x1 - x2)) + (1ll * (y1 - y2) * (y1 - y2));
}
int main() {
  scanf("%d %d %d %d %d %d", &ax, &ay, &bx, &by, &cx, &cy);
  long long ab = dist(ax, ay, bx, by);
  long long ac = dist(ax, ay, cx, cy);
  long long bc = dist(bx, by, cx, cy);
  if ((1ll * (1ll * ax * (by - cy)) + (1ll * bx * (cy - ay)) +
           (1ll * cx * (ay - by)) !=
       0) &&
      (ab == ac || ab == bc)) {
    puts("YES");
  } else {
    puts("NO");
  }
  return 0;
}