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 inline gcd(long long x, long long y) {
  return !y ? (long long)abs(x) : gcd(y, x % y);
}
long long inline lcm(long long a, long long b) {
  return ((long long)abs((a / gcd(a, b)) * b));
}
double inline cartesian_dist(double x1, double y1, double x2, double y2) {
  return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}
long long bigmod(long long b, long long p, long long m) {
  if (!p)
    return 1 % m;
  else if (p & 1)
    return (((b % m) + m) % m * bigmod(b, p - 1, m)) % m;
  else {
    long long ret = bigmod(b, p / 2, m);
    return (ret * ret) % m;
  }
}
long long inverse(long long a, long long m) { return bigmod(a, m - 2, m); }
long long extended(long long a, long long m) {
  long long oldr = a, r = m, oldans = 1, ans = 0, quotient;
  while (r) {
    quotient = oldr / r;
    oldr = oldr - r * quotient;
    swap(oldr, r);
    oldans = oldans - ans * quotient;
    swap(oldans, ans);
  }
  return ((oldans % m) + m) % m;
}
const double PI = acos(-1.0);
const double eps = 10E-12;
long long MOD = 101LL;
long long ax, ay, bx, by, cx, cy;
bool check1() {
  return (ax - bx) * (ax - bx) + (ay - by) * (ay - by) ==
         (bx - cx) * (bx - cx) + (by - cy) * (by - cy);
}
bool check2() { return (ay - by) * (ax - cx) != (ay - cy) * (ax - bx); }
int main() {
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  if (check1() && check2())
    cout << "Yes\n" << endl;
  else
    cout << "No\n" << endl;
  return 0;
}