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F - Simultaneous Swap

Score : $500$ points

Problem Statement

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.

Input

The input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\ldots$ $A_N$

$B_1$ $B_2$ $\ldots$ $B_N$

Output

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

3
1 2 1
1 1 2

Yes

Performing the operation once with $(i,j,k)=(1,2,3)$ swaps $A_1$ and $A_2$, and swaps $B_1$ and $B_3$,
making both $A$ and $B$ equal to $(2,1,1)$. Thus, you should print Yes.

3
1 2 2
1 1 2

No

There is no way to perform the operation to make $A$ and $B$ equal, so you should print No.

5
1 2 3 2 1
3 2 2 1 1

Yes

8
1 2 3 4 5 6 7 8
7 8 5 6 4 3 1 2

No