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 dis(int x1, int x2, int y1, int y2) {
  return (long long)(x1 - x2) * (x1 - x2) + (long long)(y1 - y2) * (y1 - y2);
}
int main() {
  int ax, ay, bx, by, cx, cy;
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  if ((long long)(by - ay) * (cx - bx) == (long long)(bx - ax) * (cy - by))
    cout << "NO" << endl;
  else {
    long long d1 = dis(ax, bx, ay, by);
    long long d2 = dis(bx, cx, by, cy);
    if (abs(d1 - d2) < 1e-9)
      cout << "YES" << endl;
    else
      cout << "NO" << endl;
  }
  return 0;
}