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 cross(complex<long long> a, complex<long long> b) {
  return (conj(a) * b).imag();
}
long long dis(complex<long long> a, complex<long long> b) {
  return ((a.real() - b.real()) * (a.real() - b.real())) +
         ((a.imag() - b.imag()) * (a.imag() - b.imag()));
}
int main() {
  long long x1, y1;
  cin >> x1 >> y1;
  long long x2, y2;
  cin >> x2 >> y2;
  long long x3, y3;
  cin >> x3 >> y3;
  complex<long long> a(x1, y1), b(x2, y2), c(x3, y3);
  if (dis(a, b) == dis(b, c) && cross(a - b, c - b) != 0) {
    cout << "YES\n";
  } else {
    cout << "NO\n";
  }
  return 0;
}