Score : $400$ points

Problem Statement

You are given integer sequences of length $N$ each: $A=(A_1,A_2,\cdots,A_N)$ and $B=(B_1,B_2,\cdots,B_N)$.

You can repeat the following operation any number of times.

• Choose an integer $i$ ($1 \leq i \leq N-2$) and let $x,y,z$ be the current values of $A_i,A_{i+1},A_{i+2}$, respectively. Then, replace the values of $A_i,A_{i+1},A_{i+2}$ with $z,x,y$, respectively.

Determine whether it is possible to make $A$ equal $B$.

Constraints

• $3 \leq N \leq 5000$
• $1 \leq A_i,B_i \leq 5000$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\cdots$ $A_N$

$B_1$ $B_2$ $\cdots$ $B_N$

Output

If it is possible to make $A$ equal $B$, print Yes; otherwise, print No.

4
3 1 4 5
4 1 5 3

Yes

We should do the following.

• Initially, we have $A=(3,1,4,5)$.
• Do the operation with $i=1$, making $A=(4,3,1,5)$.
• Do the operation with $i=2$, making $A=(4,5,3,1)$.
• Do the operation with $i=2$, making $A=(4,1,5,3)$.

3
1 2 2
2 1 2

Yes

3
1 2 3
2 3 4

No