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(int argc, char* argv[]) {
  long long ax, ay, bx, by, cx, cy, ab, bc;
  double slopeAB, slopeBC;
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  if (ax == cx && ay == cy) {
    cout << "Yes\n";
  } else {
    ab = (ax - bx) * (ax - bx) + (ay - by) * (ay - by);
    bc = (cx - bx) * (cx - bx) + (cy - by) * (cy - by);
    slopeAB = (double)(ay - by) / (double)(ax - bx);
    slopeBC = (double)(by - cy) / (double)(bx - cx);
    if (ab == bc && slopeAB != slopeBC) {
      cout << "Yes\n";
    } else {
      cout << "No\n";
    }
  }
  return 0;
}