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;
const int INF = 1e9 + 7;
const int maxn = 1e3 + 7;
int n, m;
long long xa, ya, xb, yb, xc, yc;
bool ok() { return (ya - yb) * (xb - xc) == (xa - xb) * (yb - yc); }
int main() {
  while (scanf("%lld%lld%lld%lld%lld%lld", &xa, &ya, &xb, &yb, &xc, &yc) !=
         EOF) {
    long long acx = xa + xc, acy = ya + yc;
    long long x1 = acx - xb * 2, y8687969 = acy - yb * 2;
    long long x2 = xa - xc, y2 = ya - yc;
    if (!ok() && x1 * x2 + y8687969 * y2 == 0)
      puts("YES");
    else
      puts("NO");
  }
  return 0;
}