Flea travel

A flea is sitting at one of the n hassocks, arranged in a circle, at the moment. After minute number k the flea jumps through k - 1 hassoсks (clockwise). For example, after the first minute the flea jumps to the neighboring hassock. You should answer: will the flea visit all the hassocks or not. We assume that flea has infinitely much time for this jumping.

Input

The only line contains single integer: 1 ≤ n ≤ 1000 — number of hassocks.

Output

Output "YES" if all the hassocks will be visited and "NO" otherwise.

Examples

Input

1

Output

YES

Input

3

Output

NO

inputFormat

Input

The only line contains single integer: 1 ≤ n ≤ 1000 — number of hassocks.

outputFormat

Output

Output "YES" if all the hassocks will be visited and "NO" otherwise.

Examples

Input

1

Output

YES

Input

3

Output

NO

样例

1

YES

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