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;
long long ax, ay, bx, by, cx, cy, flag = 0;
long long f(long long x1, long long y1, long long x2, long long y2) {
  long long res = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
  return res;
}
bool isColinear() {
  long long res1 = (by - ay) * (cx - bx);
  long long res2 = (cy - by) * (bx - ax);
  if (res1 == res2)
    return true;
  else
    return false;
}
int main() {
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  if (isColinear() == true)
    flag = 0;
  else {
    long long dis1 = f(ax, ay, bx, by);
    long long dis2 = f(bx, by, cx, cy);
    if (dis1 == dis2)
      flag = 1;
    else
      flag = 0;
  }
  if (flag == 1)
    printf("Yes\n");
  else
    printf("No\n");
}