Mapping

problem

AOR Ika made a set $S = \\ {a_1, ..., a_N \\}$ and a map $f: S → S$. $f (a_i) = b_i$. For any element $x$ in the set $S$, all maps $g, h: S → S$ satisfying $g (f (x)) = h (f (x))$ are $g (x). ) = Determine if h (x)$ is satisfied, and if not, configure one counterexample.

Example

Input

5 1 2 3 4 5 3 4 2 5 1

Output

Yes

inputFormat

Input

5 1 2 3 4 5 3 4 2 5 1

outputFormat

Output

Yes

样例

5
1 2 3 4 5
3 4 2 5 1

Yes