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 vx[3];
long long vy[3];
long long dis(long long a, long long b) {
  return (vx[a] - vx[b]) * (vx[a] - vx[b]) + (vy[a] - vy[b]) * (vy[a] - vy[b]);
}
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  for (long long i = 0; i < 3; i++) {
    cin >> vx[i] >> vy[i];
  }
  if (vx[1] - vx[0] == vx[2] - vx[1] && vy[1] - vy[0] == vy[2] - vy[1]) {
    cout << "No\n";
  } else if (dis(0, 1) == dis(1, 2))
    cout << "Yes\n";
  else
    cout << "No\n";
  return 0;
}