Score : $600$ points

Problem Statement

Given are two sequences $A$ and $B$, both of length $N$. $A$ and $B$ are each sorted in the ascending order. Check if it is possible to reorder the terms of $B$ so that for each $i$ ($1 \leq i \leq N$) $A_i \neq B_i$ holds, and if it is possible, output any of the reorderings that achieve it.

Constraints

• $1\leq N \leq 2 \times 10^5$
• $1\leq A_i,B_i \leq N$
• $A$ and $B$ are each sorted in the ascending order.
• 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 there exist no reorderings that satisfy the condition, print No.

If there exists a reordering that satisfies the condition, print Yes on the first line. After that, print a reordering of $B$ on the second line, separating terms with a whitespace.

If there are multiple reorderings that satisfy the condition, you can print any of them.

6
1 1 1 2 2 3
1 1 1 2 2 3

Yes
2 2 3 1 1 1

3
1 1 2
1 1 3

No

4
1 1 2 3
1 2 3 3

Yes
3 3 1 2