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 long long mod = 1e9 + 7;
long long a[6];
long long f(int x, int y) {
  long long ans = (a[x] - a[y]) * (a[x] - a[y]);
  ans += (a[x + 1] - a[y + 1]) * (a[x + 1] - a[y + 1]);
  return ans;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  for (int i = 0; i < 6; ++i) {
    cin >> a[i];
  }
  set<long long> s;
  s.insert(f(0, 2));
  s.insert(f(4, 2));
  long long x = (a[3] - a[1]) * (a[4] - a[2]);
  long long y = (a[5] - a[3]) * (a[2] - a[0]);
  if (x == y) {
    cout << "No" << '\n';
    ;
    return 0;
  }
  if (s.size() == 1) {
    cout << "Yes" << '\n';
    ;
  } else
    cout << "No" << '\n';
  ;
  return 0;
}