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 p[3][2];
inline long long dist(long long i, long long j) {
  return (p[i][0] - p[j][0]) * (p[i][0] - p[j][0]) +
         (p[i][1] - p[j][1]) * (p[i][1] - p[j][1]);
}
inline long long det() {
  return (p[0][0] - p[1][0]) * (p[1][1] - p[2][1]) -
         (p[0][1] - p[1][1]) * (p[1][0] - p[2][0]);
}
int main() {
  for (int i = 0; i < 3; ++i)
    for (int j = 0; j < 2; ++j) cin >> p[i][j];
  if (dist(0, 1) == dist(1, 2) && det())
    puts("Yes");
  else
    puts("No");
  return 0;
}