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 M = 100000000000000;
long long int M1 = 1000000007;
int main() {
  long long int a1, a2, b1, b2, c1, c2, x1, x2, x3, x4, x5, x6;
  double f1, f2;
  cin >> a1 >> a2 >> b1 >> b2 >> c1 >> c2;
  if (a1 == b1 && b1 == c1) {
    cout << "No" << endl;
    return 0;
  }
  x1 = pow(abs(b1 - a1), 2) + pow(abs(b2 - a2), 2);
  x2 = pow(abs(b1 - c1), 2) + pow(abs(b2 - c2), 2);
  x3 = b2 - a2;
  x4 = b1 - a1;
  x5 = b2 - c2;
  x6 = b1 - c1;
  if (x4 == 0 || x6 == 0) {
    f1 = 1;
    f2 = 2;
  } else {
    f1 = (float)x3 / x4;
    f2 = (float)x5 / x6;
  }
  if (f1 != f2 && x1 == x2)
    cout << "Yes";
  else
    cout << "No";
  cout << endl;
}