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;
struct po {
  long long x, y;
} A, B, C, n, m;
int main() {
  scanf("%I64d%I64d%I64d%I64d%I64d%I64d", &A.x, &A.y, &B.x, &B.y, &C.x, &C.y);
  n.x = B.x - A.x;
  n.y = B.y - A.y;
  m.x = C.x - B.x;
  m.y = C.y - B.y;
  if ((n.x * n.x + n.y * n.y == m.x * m.x + m.y * m.y) &&
      (n.x * m.y != n.y * m.x))
    puts("YES");
  else
    puts("NO");
  return 0;
}