At a geometry lesson Gerald was given a task: to get vector B out of vector A. Besides, the teacher permitted him to perform the following operations with vector А:

  * Turn the vector by 90 degrees clockwise.
  * Add to the vector a certain vector C.



Operations could be performed in any order any number of times.

Can Gerald cope with the task?

Input

The first line contains integers x1 и y1 — the coordinates of the vector A ( - 108 ≤ x1, y1 ≤ 108). The second and the third line contain in the similar manner vectors B and C (their coordinates are integers; their absolute value does not exceed 108).

Output

Print "YES" (without the quotes) if it is possible to get vector B using the given operations. Otherwise print "NO" (without the quotes).

Examples

Input

0 0
1 1
0 1


Output

YES


Input

0 0
1 1
1 1


Output

YES


Input

0 0
1 1
2 2


Output

NO
#include <bits/stdc++.h>
using namespace std;
struct pt {
  long long x, y;
  pt(long long xx, long long yy) { x = xx, y = yy; }
  pt() {}
  pt operator+(pt b) { return pt(x + b.x, y + b.y); }
  pt gir() { return pt(-y, x); }
  bool operator==(pt b) { return x == b.x and y == b.y; }
};
bool go(long long x1, long long y1, long long z1, long long x2, long long y2,
        long long z2) {
  long long det = x1 * y2 - x2 * y1;
  long long a = z1 * y2 - y1 * z2;
  long long b = x1 * z2 - x2 * z1;
  if (det != 0)
    return a % det == 0 and b % det == 0;
  else
    return z1 == z2 and z1 == 0;
}
int main() {
  pt a, b, c;
  cin >> a.x >> a.y;
  cin >> b.x >> b.y;
  cin >> c.x >> c.y;
  pt d = c.gir();
  bool vale = a == b;
  if (go(c.x, d.x, b.x - a.x, c.y, d.y, b.y - a.y)) vale = true;
  a = a.gir();
  if (go(c.x, d.x, b.x - a.x, c.y, d.y, b.y - a.y)) vale = true;
  a = a.gir();
  if (go(c.x, d.x, b.x - a.x, c.y, d.y, b.y - a.y)) vale = true;
  a = a.gir();
  if (go(c.x, d.x, b.x - a.x, c.y, d.y, b.y - a.y)) vale = true;
  if (vale)
    cout << "YES\n";
  else
    cout << "NO\n";
}
