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>
const int inf = 0x3f3f3f3f;
const long long INF = 0x3f3f3f3f3f3f3f3f;
const double eps = 1e-8;
using namespace std;
const int maxn = 1000 + 10;
struct acmer {
  int x, y;
};
int main() {
  acmer a, b, c;
  scanf("%d%d%d%d%d%d", &a.x, &a.y, &b.x, &b.y, &c.x, &c.y);
  bool flag = 1;
  if ((long long)(c.x - b.x) * (b.y - a.y) ==
      (long long)(c.y - b.y) * (b.x - a.x))
    flag = 0;
  if (flag == 0)
    puts("No");
  else {
    long long x = (long long)(a.x - b.x) * (a.x - b.x) +
                  (long long)(a.y - b.y) * (a.y - b.y);
    long long y = (long long)(b.x - c.x) * (b.x - c.x) +
                  (long long)(b.y - c.y) * (b.y - c.y);
    if (x == y)
      puts("Yes");
    else
      puts("No");
  }
  return 0;
}