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 MAX = 10010;
const double eps = 1e-6;
int n, m;
struct Point {
  long long x, y;
} p1, p2, p3;
long long crosspro(Point a, Point b, Point c) {
  long long sum =
      a.x * b.y + b.x * c.y + c.x * a.y - b.x * a.y - c.x * b.y - a.x * c.y;
  return sum;
}
long long dist(Point a, Point b) {
  return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
}
int main() {
  int i, j, k;
  while (~scanf("%lld%lld%lld%lld%lld%lld", &p1.x, &p1.y, &p2.x, &p2.y, &p3.x,
                &p3.y)) {
    long long ans = crosspro(p1, p2, p3);
    if (ans) {
      if (dist(p1, p2) == dist(p2, p3))
        printf("Yes\n");
      else
        printf("No\n");
    } else
      printf("No\n");
  }
  return 0;
}