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;
double dist(double x1, double y1, double x2, double y2) {
  double d = (double)((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
  return d;
}
void solve() {
  double ax, ay, bx, by, cx, cy;
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  double lenab = dist(ax, ay, bx, by);
  double lenbc = dist(bx, by, cx, cy);
  double lenac = dist(cx, cy, ax, ay);
  if (sqrt(lenab) != sqrt(lenbc)) {
    cout << "No\n";
    return;
  }
  long long ar = ax * (by - cy) + bx * (cy - ay) + cx * (ay - by);
  if (ar == 0) {
    cout << "No\n";
    return;
  }
  cout << "Yes\n";
  return;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int t = 1;
  while (t--) {
    solve();
  }
  return 0;
}