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;
pair<int, int> a, b, c;
long long dist(pair<int, int> a, pair<int, int> b) {
  return 1LL * (a.first - b.first) * (a.first - b.first) +
         1LL * (a.second - b.second) * (a.second - b.second);
}
long long area(pair<int, int> a, pair<int, int> b, pair<int, int> c) {
  return 1LL * a.first * b.second + 1LL * a.second * c.first +
         1LL * b.first * c.second - 1LL * b.second * c.first -
         1LL * a.second * b.first - 1LL * a.first * c.second;
}
int main() {
  cin >> a.first >> a.second >> b.first >> b.second >> c.first >> c.second;
  if (dist(a, b) == dist(b, c) && area(a, b, c) != 0)
    cout << "Yes\n";
  else
    cout << "No\n";
  return 0;
}