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, cx, cy;
long long AX[4], AY[4], CX[4], CY[4];
bool judge_51nod(long long ax, long long ay, long long cx, long long cy) {
  long long zi1 = abs((bx - ax) * cx + (by - ay) * cy);
  long long zi2 = abs((by - ay) * cx - (bx - ax) * cy);
  long long mu = abs(cx * cx + cy * cy);
  if (mu)
    if (zi1 % mu || zi2 % mu) return 0;
  return 1;
}
bool judge(long long ax, long long ay, long long cx, long long cy) {
  if (cx == 0 && cy == 0) return ax == bx && ay == by;
  long long zi1 = abs((bx - ax) * cx + (by - ay) * cy);
  long long zi2 = abs((by - ay) * cx - (bx - ax) * cy);
  long long mu = abs(cx * cx + cy * cy);
  return zi1 % mu == 0 && zi2 % mu == 0;
}
int main() {
  cin >> ax >> ay >> bx >> by >> cx >> cy;
  AX[0] = ax, AY[0] = ay;
  AX[1] = -ay, AY[1] = ax;
  AX[2] = -ax, AY[2] = -ay;
  AX[3] = ay, AY[3] = -ax;
  CX[0] = cx, CY[0] = cy;
  CX[1] = -cy, CY[1] = cx;
  CX[2] = -cx, CY[2] = -cy;
  CX[3] = cy, CY[3] = -cx;
  for (int i = 0; i < 4; i++)
    for (int j = 0; j < 4; j++)
      if (judge(AX[i], AY[i], CX[j], CY[j])) return cout << "YES", 0;
  cout << "NO";
}
