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;
int dy[] = {0, 0, 1, -1};
int dx[] = {1, -1, 0, 0};
int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
int lcm(int a, int b) { return a / gcd(a, b) * b; }
double dist(pair<double, double> p, pair<double, double> q) {
  return sqrt(pow(p.first - q.first, 2) + pow(p.second - q.second, 2));
}
double dot(pair<double, double> p, pair<double, double> q) {
  return p.first * q.first + p.second * q.second;
}
pair<double, double> a, b, c;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  for (int i = 0; i < (3); ++i) {
    double x, y;
    cin >> x >> y;
    if (i == 0)
      a = make_pair(x, y);
    else if (i == 1)
      b = make_pair(x, y);
    else
      c = make_pair(x, y);
  }
  double distba = dist(a, b);
  double distbc = dist(b, c);
  if (distba != distbc) {
    cout << "No" << endl;
  } else {
    if ((b.first - c.first) * (b.second - a.second) ==
        (b.second - c.second) * (b.first - a.first)) {
      cout << "No" << endl;
    } else
      cout << "Yes" << endl;
  }
  return 0;
}