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 x[3], y[3], h, k, a[3][3];
int main(int argc, const char* argv[]) {
  for (int i = 0; i < 3; i++) cin >> x[i] >> y[i];
  long double a1 =
      (x[0] - x[1]) * ((x[0] - x[1])) + (y[0] - y[1]) * (y[0] - y[1]);
  a1 = sqrt(a1);
  long double a2 =
      (x[1] - x[2]) * ((x[1] - x[2])) + (y[1] - y[2]) * (y[1] - y[2]);
  a2 = sqrt(a2);
  long double a3 =
      (x[0] - x[2]) * ((x[0] - x[2])) + (y[0] - y[2]) * (y[0] - y[2]);
  a3 = sqrt(a3);
  if (a1 == a2 && a1 + a2 != a3)
    cout << "Yes\n";
  else
    cout << "No\n";
  return 0;
}