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;
long long Ax, Ay, Bx, By, x, y;
long long tmpAx, tmpAy;
bool mod(long long opa, long long opb) {
  if (opa % opb) return false;
  return true;
}
bool check2() {
  long long A = tmpAx, B = tmpAy;
  long long tmp = A * y - B * x, op = y * y + x * x;
  long long tmp1 = A * x + B * y, op1 = x * x + y * y;
  if (op == 0) return A == 0 && B == 0;
  if (tmp % op == 0 && tmp1 % op1 == 0) return true;
  return false;
}
bool check() {
  tmpAx = Ax - Bx;
  tmpAy = Ay - By;
  if (check2()) return true;
  tmpAx = Ax + Bx;
  tmpAy = Ay + By;
  if (check2()) return true;
  tmpAx = Ax - By;
  tmpAy = Ay + Bx;
  if (check2()) return true;
  tmpAx = Ax + By;
  tmpAy = Ay - Bx;
  if (check2()) return true;
  return false;
}
int main() {
  scanf("%I64d%I64d", &Ax, &Ay);
  scanf("%I64d%I64d", &Bx, &By);
  scanf("%I64d%I64d", &x, &y);
  if (check())
    printf("YES");
  else
    printf("NO");
  return 0;
}
