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 Z = (int)1e5 + 111;
const int inf = (int)1e9 + 111;
const long long llinf = (long long)1e18 + 5;
const int MOD = (int)1e9 + 7;
long double dist(long double X1, long double Y1, long double X2,
                 long double Y2) {
  return sqrt((X1 - X2) * (X1 - X2) + (Y1 - Y2) * (Y1 - Y2));
}
int main() {
  srand(time(0));
  ios_base::sync_with_stdio(false);
  long double ax, ay, bx, by, cx, cy;
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  if (ax == bx && bx == cx) {
    cout << "No";
    return 0;
  }
  if (ay == by && by == cy) {
    cout << "No";
    return 0;
  }
  long double k = (long double)(ay - by) / (ax - bx);
  long double b = ay - k * ax;
  if (cy == k * cx + b) {
    cout << "No";
    return 0;
  }
  if (dist(ax, ay, bx, by) == dist(bx, by, cx, cy)) {
    cout << "Yes";
  } else {
    cout << "No";
  }
  return 0;
}