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 pow(long long a) { return a * a; }
int main() {
  long long ax, ay, bx, by, cx, cy;
  scanf("%I64d%I64d%I64d%I64d%I64d%I64d", &ax, &ay, &bx, &by, &cx, &cy);
  bool hasAns = false;
  if (pow(ax - bx) + pow(ay - by) == pow(bx - cx) + pow(by - cy)) hasAns = true;
  long long x1 = ax - bx, y1 = ay - by;
  long long x2 = bx - cx, y2 = by - cy;
  if (x2 * y1 == x1 * y2) hasAns = false;
  if (hasAns)
    printf("YES\n");
  else
    printf("NO\n");
  return 0;
}