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;
void inn(long long int &ix) { scanf("%lld", &ix); }
void inn(long long int &ix, long long int &iy) { scanf("%lld%lld", &ix, &iy); }
void inn(int &ix) { scanf("%d", &ix); }
void inn(int &ix, int &iy) { scanf("%d%d", &ix, &iy); }
void inn(long double &ix) { scanf("%Lf", &ix); }
void outt(long long int ix) { printf("%lld", ix); }
void outt(long long int ix, char cx) { printf("%lld%c", ix, cx); }
void outt(int ix) { printf("%d", ix); }
void outt(int ix, char cx) { printf("%d%c", ix, cx); }
void outt(long double ix, char cx) { printf("%.12Lf%c", ix, cx); }
void outt(long double ix) { printf("%.12Lf", ix); }
void outt(pair<long long int, long long int> x) {
  cout << '{' << x.first << ',' << x.second << '}' << endl;
}
const int MM = 1200000;
long long int m, n, k, p1, p2, p3, p, f, a[MM];
string s, s1, s2;
long long int isL(long long int Ax, long long int Ay, long long int Bx,
                  long long int By, long long int Cx, long long int Cy) {
  return (Ax * (By - Cy) + Bx * (Cy - Ay) + Cx * (Ay - By));
}
long double eps = 0.000001;
int main() {
  long long int t;
  long long int x1, x2, x3, y1, y2, y3;
  cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3;
  p1 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
  p2 = (x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2);
  p = (x1 - x3) * (x1 - x3) + (y1 - y3) * (y1 - y3);
  if (p1 == p2 && isL(x1, y1, x2, y2, x3, y3) != 0)
    cout << "Yes";
  else
    cout << "No";
  return 0;
}