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 dr[] = {-1, 0, 1, 0, -1, -1, 1, 1};
const int dc[] = {0, -1, 0, 1, -1, 1, -1, 1};
long long ax, ay, bx, by, cx, cy;
long long dist(long long x1, long long y1, long long x2, long long y2) {
  return ((x1 - x2) * (x1 - x2)) + ((y1 - y2) * (y1 - y2));
}
int main() {
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  if (dist(ax, ay, bx, by) != dist(bx, by, cx, cy)) {
    cout << "No\n";
    return 0;
  }
  if (ax - bx == bx - cx && ay - by == by - cy)
    cout << "No\n";
  else if (ax - cx == cx - bx && ay - cy == cy - by)
    cout << "No\n";
  else if (bx - ax == ax - cx && by - ay == ay - cy)
    cout << "No\n";
  else if (bx - cx == cx - ax && by - cy == cy - ay)
    cout << "No\n";
  else if (cx - ax == ax - cx && cy - ay == ay - cy)
    cout << "No\n";
  else if (cx - bx == bx - cx && cy - by == by - cy)
    cout << "No\n";
  else
    cout << "Yes\n";
  return 0;
}