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;
struct p {
  long long x, y;
} po[10];
bool cmp(p a, p b) {
  if (a.x != b.x)
    return a.x < b.x;
  else
    return a.y < b.y;
}
long long dist(p a, p b) {
  return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
}
int main() {
  cin >> po[0].x >> po[0].y >> po[1].x >> po[1].y >> po[2].x >> po[2].y;
  long long dis[10];
  dis[1] = dist(po[1], po[2]);
  dis[2] = dist(po[0], po[1]);
  dis[0] = dist(po[0], po[2]);
  long long dx1 = po[0].x - po[1].x, dx2 = po[0].x - po[2].x,
            dx3 = po[1].x - po[2].x;
  long long dy1 = po[0].y - po[1].y, dy2 = po[0].y - po[2].y,
            dy3 = po[1].y - po[2].y;
  if ((dis[1] == dis[2]) && (dx1 * dy3 - dx3 * dy1 != 0)) {
    cout << "Yes" << endl;
  } else
    cout << "No" << endl;
  return 0;
}