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;
int main() {
  long long x1, y1, x2, y2, x3, y3;
  scanf("%I64d%I64d", &x1, &y1);
  scanf("%I64d%I64d", &x2, &y2);
  scanf("%I64d%I64d", &x3, &y3);
  bool flag = false, flag2 = false, flag3 = false, flag4 = false;
  long long m = x2 - x1, n = y2 - y1;
  if (x3 == 0 && y3 == 0) {
    if (m == 0 && n == 0)
      flag = true;
    else
      flag = false;
  } else {
    long long a = x3 * x3, b = y3 * y3;
    if ((y3 * m - x3 * n) % (a + b) == 0 && (x3 * m + y3 * n) % (a + b) == 0)
      flag = true;
    else
      flag = false;
  }
  m = x2 + y1, n = y2 - x1;
  if (x3 == 0 && y3 == 0) {
    if (m == 0 && n == 0)
      flag2 = true;
    else
      flag2 = false;
  } else {
    long long a = x3 * x3, b = y3 * y3;
    if ((y3 * m - x3 * n) % (a + b) == 0 && (x3 * m + y3 * n) % (a + b) == 0)
      flag2 = true;
    else
      flag2 = false;
  }
  m = x2 + x1, n = y2 + y1;
  if (x3 == 0 && y3 == 0) {
    if (m == 0 && n == 0)
      flag3 = true;
    else
      flag3 = false;
  } else {
    long long a = x3 * x3, b = y3 * y3;
    if ((y3 * m - x3 * n) % (a + b) == 0 && (x3 * m + y3 * n) % (a + b) == 0)
      flag3 = true;
    else
      flag3 = false;
  }
  m = x2 - y1, n = y2 + x1;
  if (x3 == 0 && y3 == 0) {
    if (m == 0 && n == 0)
      flag4 = true;
    else
      flag4 = false;
  } else {
    long long a = x3 * x3, b = y3 * y3;
    if ((y3 * m - x3 * n) % (a + b) == 0 && (x3 * m + y3 * n) % (a + b) == 0)
      flag4 = true;
    else
      flag4 = false;
  }
  flag || flag2 || flag3 || flag4 ? printf("YES\n") : printf("NO\n");
  return 0;
}
