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;
long long modular_pow(long long base, long long exponent, long long modulus) {
  long long result = 1;
  while (exponent > 0) {
    if (exponent % 2 == 1) result = (result * base) % modulus;
    exponent = exponent >> 1;
    base = (base * base) % modulus;
  }
  return result;
}
void computePrefixTable(string pat, vector<int>& v) {
  int len = 0;
  v[0] = 0;
  int i = 1;
  while (i < pat.size()) {
    if (pat[i] == pat[len]) {
      len++;
      v[i] = len;
      i++;
    } else {
      if (len != 0) {
        len = v[len - 1];
      } else {
        v[i] = 0;
        i++;
      }
    }
  }
}
long long countDistinctSubstrings(string s, int i, int j) {
  string r = s.substr(i, j - i + 1);
  vector<int> v(r.size(), 0);
  computePrefixTable(r, v);
  long long tot = v.size() * (v.size() + 1) / 2;
  for (int k = 0; k < v.size(); k++) {
    tot -= v[k];
  }
  return tot;
}
long long gcd(long long a, long long b) { return (b == 0) ? a : gcd(b, a % b); }
long long numDigits(long long i) {
  return i > 0 ? (long long)log10((double)i) + 1 : 1;
}
long long dist(long long ax, long long ay, long long bx, long long by) {
  return (bx - ax) * (bx - ax) + (by - ay) * (by - ay);
}
int main() {
  ios_base::sync_with_stdio(false);
  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)) {
    cout << "No" << endl;
    return 0;
  }
  if (4 * dist(ax, ay, bx, by) == dist(ax, ay, cx, cy)) {
    cout << "No" << endl;
    return 0;
  }
  cout << "Yes" << endl;
}