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() {
  long double a, b, x, y, v, res, mi = 0.0000000001, t1, t2, c, d, vpr;
  long double xb, yb, xc, yc;
  int n, i, j, k, p = 0;
  cin >> c >> d >> a >> b >> x >> y;
  t1 = sqrt((x - a) * (x - a) + (y - b) * (y - b));
  t2 = sqrt((c - a) * (c - a) + (d - b) * (d - b));
  xb = a - c;
  yb = b - d;
  xc = x - c;
  yc = y - d;
  vpr = xb * yc - yb * xc;
  if (abs(t1 - t2) <= mi && abs(vpr) > mi)
    cout << "Yes";
  else
    cout << "No";
  return 0;
}