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 int N = 100020;
bool sortinrev(const pair<int, int> &a, const pair<int, int> &b) {
  return (a.first > b.first);
}
bool sortbysecdesc(const pair<int, int> &a, const pair<int, int> &b) {
  return a.second > b.second;
}
bool sortbysec(const pair<int, int> &a, const pair<int, int> &b) {
  return (a.second < b.second);
}
long long int pow(long long int x, long long int y) {
  long long int res = 1;
  while (y > 0) {
    if (y & 1) res = ((res) * (x));
    res %= N;
    y = y >> 1;
    x = ((x) * (x));
  }
  return res;
}
int powm(int x, int y, int p) {
  int res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long int power(long long int a, long long int b) {
  if (b == 1) return a;
  if (b == 0) return 1;
  long long int m1 = power(a, b / 2);
  if (b % 2) return m1 * m1 * a;
  return m1 * m1;
}
void codeit() {
  long long x1, y1, x2, y2, x3, y3;
  cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3;
  long double d1, d2, d3;
  d1 = sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
  d2 = sqrt((x2 - x3) * (x2 - x3) + (y2 - y3) * (y2 - y3));
  d3 = sqrt((x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1));
  if ((long long)(x2 - x1) * (y3 - y1) == (long long)(y2 - y1) * (x3 - x1)) {
    cout << "No";
    return;
  }
  if (d1 == d2) {
    cout << "Yes" << '\n';
    return;
  } else {
    cout << "No" << '\n';
    return;
  }
  return;
}
int main() {
  long long int tt;
  tt = 1;
  for (int i = 0; i < tt; i++) codeit();
}