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 int MAXN = 2e5 + 10;
long long dist2(long long x1, long long y1, long long x2, long long y2) {
  return (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
}
int main() {
  long long xa, ya, xb, yb, xc, yc;
  cin >> xa >> ya >> xb >> yb >> xc >> yc;
  if (abs((yb - ya) * (xc - xb)) == abs((yc - yb) * (xb - xa)) &&
      abs(((yb - yc) * (xa - xc))) == abs((ya - yc) * (xb - xc)))
    cout << "No\n";
  else {
    if (dist2(xa, ya, xb, yb) == dist2(xb, yb, xc, yc))
      cout << "Yes\n";
    else
      cout << "No\n";
  }
  return 0;
}