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 inf = (1e9) + 7;
long long sqr(long long x) { return x * x; }
int main() {
  long long ax, ay;
  long long bx, by;
  long long cx, cy;
  cin >> ax >> ay;
  cin >> bx >> by;
  cin >> cx >> cy;
  long long d1 = sqr(ax - bx) + sqr(ay - by);
  long long d2 = sqr(cx - bx) + sqr(cy - by);
  if (d1 == d2 and ((ay - by) * (bx - cx) != (by - cy) * (ax - bx)))
    printf("Yes\n");
  else
    printf("No\n");
}