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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  double ax, ay, bx, by, cx, cy;
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  long long int dist1 = ((by - ay) * (by - ay)) + ((bx - ax) * (bx - ax));
  long long int dist2 = ((cy - by) * (cy - by)) + ((cx - bx) * (cx - bx));
  double slope1;
  double slope2;
  if (bx == ax)
    slope1 = 12312414134134;
  else {
    slope1 = (by - ay) / (bx - ax);
  }
  if (cx == bx)
    slope2 = 12312414134134;
  else
    slope2 = (cy - by) / (cx - bx);
  if (dist1 == dist2 && slope1 != slope2) {
    cout << "yes\n";
  } else
    cout << "no\n";
  return 0;
}