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
def g():
    return map(int,raw_input().split())
a,b=g()
c,d=g()
e,f=g()
z,r,i=f*f+e*e,0,4
while i:
    i-=1
    a,b=b,-a
    x,y=c-a,d-b
    r |= (z==0 and x==0 and y==0) | (z and (x*e+y*f)%z==0 and (y*e-x*f)%z==0)
print "YES" if r else "NO"