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;
bool check_prime(long long n) {
  long long flag = 0;
  for (long long i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      flag = 1;
      break;
    }
  }
  if (n == 1)
    return false;
  else if (flag == 0 || n == 2 || n == 3) {
    return true;
  } else {
    return false;
  }
}
long long BE(long long x, long long n, long long m) {
  long long result = 1;
  while (n > 0) {
    if (n % 2 == 1) result = result * x % m;
    x = x * x % m;
    n = n / 2;
  }
  return result;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(0);
  long double a, b, c, d, e, f;
  cin >> a >> b >> c >> d >> e >> f;
  if (((a - c) * (a - c) + (b - d) * (b - d) !=
       (e - c) * (e - c) + (f - d) * (f - d)) ||
      ((a + e) / 2.0 == c && (b + f) / 2.0 == d))
    cout << "No" << '\n';
  else
    cout << "Yes" << '\n';
  return 0;
}