You are given two sequences of $N$ numbers: $A=(A_1,A_2,\ldots,A_N)$ and $B=(B_1,B_2,\ldots,B_N)$. Takahashi can repeat the following operation any number of times (possibly zero). > Choose three pairwise distinct integers $i$, $j$, and $k$ between $1$ and $N$. > Swap the $i$\-th and $j$\-th elements of $A$, and swap the $i$\-th and $k$\-th elements of $B$. If there is a way for Takahashi to repeat the operation to make $A$ and $B$ equal, print `Yes`; otherwise, print `No`. Here, $A$ and $B$ are said to be equal when, for every $1\leq i\leq N$, the $i$\-th element of $A$ and that of $B$ are equal. ### Constraints - $3 \leq N \leq 2\times 10^5$ - $1\leq A_i,B_i\leq N$ - All values in the input are integers.

The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ $B_1$ $B_2$ $\ldots$ $B_N$

Print `Yes` if there is a way for Takahashi to repeat the operation to make $A$ and $B$ equal, and print `No` otherwise.