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 long mod = 1e6 + 7;
const long eps = 1e-10;
const long long oo = 1e9;
const long maxn = 2500;
const long maxm = 20000;
const double pi = atan(1) * 4;
inline long gcd(long a, long b) {
  long r;
  while (b) {
    r = a % b;
    a = b;
    b = r;
  }
  return a;
}
inline long lcm(long a, long b) { return a / gcd(a, b) * b; }
inline void swap(long long &a, long long &b) {
  long long tmp = a;
  a = b;
  b = tmp;
}
long long ax, ay, bx, by, cx, cy;
void fileio() {
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  double sideAB = sqrt(pow(bx - ax, 2) + pow(by - ay, 2));
  double sideCB = sqrt(pow(bx - cx, 2) + pow(by - cy, 2));
  double sideAC = sqrt(pow(cx - ax, 2) + pow(cy - ay, 2));
  if (sideAB + sideAC > sideCB and sideAB + sideCB > sideAC and
      sideAC + sideCB > sideAB) {
    if (fabs(sideAB - sideCB) <= eps)
      cout << "Yes";
    else
      cout << "No";
    return 0;
  }
  cout << "No";
  return 0;
}