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 int power(long long int a, long long int b, long long int m) {
  long long int pp = (b == 0) ? 1 : power(a, b >> 1, m);
  pp = (pp * pp) % m;
  if (b & 1) pp = (pp * a) % m;
  return pp;
}
long long int dist(long long int a, long long int b, long long int c,
                   long long int d) {
  return ((a - c) * (a - c) + (b - d) * (b - d));
}
signed main() {
  long long int a, b, c, d, e, f;
  scanf("%lld", &(a));
  scanf("%lld", &(b));
  scanf("%lld", &(c));
  scanf("%lld", &(d));
  scanf("%lld", &(e));
  scanf("%lld", &(f));
  if ((d - b) * (e - c) == (c - a) * (f - d))
    puts("No");
  else {
    if (dist(a, b, c, d) == dist(c, d, e, f))
      puts("Yes");
    else
      puts("No");
  }
  return 0;
}