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 check(x, y, p, q):
    if x == 0 and y == 0:
        return True
    elif p * p + q * q != 0 and (x * q - y * p) % (p * p + q * q) == 0 and (x * p + y * q) % (p * p + q * q) == 0:
        return True
    else:
        return False

x, y = map(int, raw_input().split())
a, b = map(int, raw_input().split())
p, q = map(int, raw_input().split())
if check(x - a, y - b, p, q) or check(x - b, y + a, p, q) or check(x + b, y - a, p, q) or check(x + a, y + b, p, q):
    print "YES"
else:
    print "NO"