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;
int const INF = numeric_limits<int>::max();
long long const LLINF = numeric_limits<long long>::max();
long double const EPS = 1e-9;
long long det(long long xa, long long ya, long long xb, long long yb,
              long long xc, long long yc) {
  return xa * yb + xb * yc + xc * ya - xc * yb - xa * yc - xb * ya;
}
long long dist2(long long xa, long long ya, long long xb, long long yb) {
  return (xa - xb) * (xa - xb) + (ya - yb) * (ya - yb);
}
int main() {
  ios::sync_with_stdio(false);
  long long xa, xb, xc, ya, yb, yc;
  cin >> xa >> ya >> xb >> yb >> xc >> yc;
  if (det(xa, ya, xb, yb, xc, yc) == 0)
    cout << "No" << endl;
  else if (dist2(xa, ya, xb, yb) == dist2(xb, yb, xc, yc))
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
  return 0;
}