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>
struct Vector {
  long long int x, y;
  Vector() : x(0), y(0) {}
  Vector(const Vector& a, const Vector& b) : x(b.x - a.x), y(b.y - a.y) {}
  double len() { return hypot(x, y); }
};
long long int cross(Vector& a, Vector& b);
long long int cross(Vector& a, Vector& b) { return a.x * b.y - a.y * b.x; }
int main() {
  Vector a, b, c;
  std::cin >> a.x >> a.y >> b.x >> b.y >> c.x >> c.y;
  Vector ba(b, a), bc(b, c);
  if ((ba.x * ba.x + ba.y * ba.y != bc.x * bc.x + bc.y * bc.y) ||
      (cross(ba, bc) == 0))
    std::cout << "No";
  else
    std::cout << "Yes";
  return 0;
}