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;
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
  os << "sz:" << v.size() << "\n[";
  for (const auto& p : v) {
    os << p << ",";
  }
  os << "]\n";
  return os;
}
template <typename S, typename T>
ostream& operator<<(ostream& os, const pair<S, T>& p) {
  os << "(" << p.first << "," << p.second << ")";
  return os;
}
constexpr ll MOD = (ll)1e9 + 7LL;
template <typename T>
constexpr T INF = numeric_limits<T>::max() / 100;
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  ll ax, ay, bx, by, cx, cy;
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  const ll d1 = (bx - ax) * (bx - ax) + (by - ay) * (by - ay);
  const ll d2 = (bx - cx) * (bx - cx) + (by - cy) * (by - cy);
  if (d1 == d2) {
    const ll dx1 = bx - ax;
    const ll dy1 = by - ay;
    const ll dx2 = cx - ax;
    const ll dy2 = cy - ay;
    if (dx1 * dy2 == dx2 * dy1) {
      cout << "No" << endl;
    } else {
      cout << "Yes" << endl;
    }
  } else {
    cout << "No" << endl;
  }
  return 0;
}