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F - Swap and Sort

Score : $500$ points

Problem Statement

We have a permutation $P=(P_1,P_2,\ldots,P_N)$ of $(1,2,\ldots,N)$.

There are $M$ kinds of operations available to you. Operation $i$ swaps the $a_i$-th and $b_i$-th elements of $P$.

Is it possible to sort $P$ in ascending order by doing at most $5\times 10^5$ operations in total in any order?

If it is possible, give one such sequence of operations. Otherwise, report so.

Constraints

• $2\leq N \leq 1000$
• $P$ is a permutation of $(1,2,\ldots,N)$.
• $1\leq M \leq \min(2\times 10^5, \frac{N(N-1)}{2})$
• $1\leq a_i \lt b_i\leq N$
• $(a_i,b_i)\neq (a_j,b_j)$ if $i\neq j$.
• All values in input are integers.

---

Input

Input is given from Standard Input in the following format:

$N$

$P_1$ $P_2$ $\ldots$ $P_N$

$M$

$a_1$ $b_1$

$a_2$ $b_2$

$\vdots$

$a_M$ $b_M$

Output

If it is possible to sort $P$ in ascending order, print the following:

``` $K$ $c_1$ $c_2$ $\ldots$ $c_K$ ```

Here, $K$ represents the number of operations to do, and $c_i$ $(1\leq i \leq K)$ means the $i$-th operation to do is Operation $c_i$.
Note that $0\leq K \leq 5\times 10^5$ must hold.

If it is impossible to sort $P$ in ascending order, print -1.

---

6
5 3 2 4 6 1
4
1 5
5 6
1 2
2 3

3
4 2 1

$P$ changes as follows: $(5,3,2,4,6,1)\to (5,2,3,4,6,1)\to (5,2,3,4,1,6)\to (1,2,3,4,5,6)$.

---

5
3 4 1 2 5
2
1 3
2 5

-1

We cannot sort $P$ in ascending order.

---

4
1 2 3 4
6
1 2
1 3
1 4
2 3
2 4
3 4

0

$P$ may already be sorted in ascending order.

Additionally, here is another accepted output:

``` 4 5 5 5 5 ```

Note that it is not required to minimize the number of operations.