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 double eps = 0.000001;
const long double pi = acos(-1);
const int maxn = 1e7 + 9;
const int mod = 1e9 + 7;
const long long MOD = 1e18 + 9;
const long long INF = 1e18 + 123;
const int inf = 2e9 + 11;
const int minn = 1e5 + 9;
const int N = 5e3 + 123;
const int NN = 5e5 + 123;
const int PRI = 555557;
const int pri = 997;
int tests = 1;
int n, m, k, a[NN], cnt, ans;
long long dist(long long x1, long long y1, long long x2, long long y2) {
  return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
}
inline void Solve() {
  long long ax, ay, bx, by, cx, cy;
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  if (dist(ax, ay, bx, by) == dist(bx, by, cx, cy) &&
      !(bx - ax == cx - bx && by - ay == cy - by))
    cout << "Yes";
  else
    cout << "No";
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0);
  while (tests--) {
    Solve();
  }
}