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;
struct Point {
  long long x;
  long long y;
  Point(long long x, long long y) : x(x), y(y) {}
};
struct Vect {
  int x;
  int y;
  Vect(Point A, Point B) : x(B.x - A.x), y(B.y - A.y) {}
  long long operator*(const Vect &v) const {
    return (long long)x * v.y - (long long)y * v.x;
  }
};
int main() {
  long long ax, ay, bx, by, cx, cy;
  scanf("%lld %lld %lld %lld %lld %lld", &ax, &ay, &bx, &by, &cx, &cy);
  Point A(ax, ay), B(bx, by), C(cx, cy);
  Vect AB(A, B);
  Vect BC(B, C);
  if (AB * BC == 0)
    printf("No");
  else if ((ax - bx) * (ax - bx) + (ay - by) * (ay - by) !=
           (bx - cx) * (bx - cx) + (by - cy) * (by - cy))
    printf("No");
  else
    printf("Yes");
  return 0;
}