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 main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int cases = 1;
  while (cases--) {
    long long int a, b, x, y, m, n;
    cin >> a >> b >> x >> y >> m >> n;
    long long int d1 = (a - x) * (a - x) + (b - y) * (b - y);
    long long int d2 = (x - m) * (x - m) + (y - n) * (y - n);
    long long int t1 = (n - b) * (x - a);
    long long int t2 = (m - a) * (y - b);
    if (d1 != d2 || t1 == t2) {
      cout << "NO\n";
    } else
      cout << "YES\n";
  }
  return 0;
}