#D6828. Vectors
Vectors
Vectors
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
inputFormat
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).
outputFormat
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
样例
0 0
1 1
0 1
YES