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C. Vectors

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAt 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 *x* _{1} и *y* _{1} — the coordinates of the vector *A* ( - 10^{8} ≤ *x* _{1}, *y* _{1} ≤ 10^{8}). 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 10^{8}).

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

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