CF1698F.Equal Reversal

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题目描述

There is an array $a$ of length $n$ . You may perform the following operation on it:

Choose two indices $l$ and $r$ where $1 \le l \le r \le n$ and $a_l = a_r$ . Then, reverse the subsegment from the $l$ -th to the $r$ -th element, i. e. set $[a_l, a_{l + 1}, \ldots, a_{r - 1}, a_r]$ to $[a_r, a_{r-1}, \ldots, a_{l+1}, a_l]$ .

You are also given another array $b$ of length $n$ which is a permutation of $a$ . Find a sequence of at most $n^2$ operations that transforms array $a$ into $b$ , or report that no such sequence exists.

输入格式

Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 100$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $n$ ( $1 \le n \le 500$ ) — the length of array $a$ and $b$ .

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le n$ ) — elements of the array $a$ .

The third line of each test case contains $n$ integers $b_1, b_2, \ldots, b_n$ ( $1 \le b_i \le n$ ) — elements of the array $b$ .

It is guaranteed that $b$ is a permutation of $a$ .

It is guaranteed that the sum of $n$ over all test cases does not exceed $500$ .

输出格式

For each test case, output "NO" (without quotes) if it is impossible to turn $a$ into $b$ using at most $n^2$ operations.

Otherwise, output "YES" (without quotes). Then output an integer $k$ ( $0 \leq k \leq n^2$ ) denoting the number of operations you will perform. Note that you don't have to minimize the number of operations.

Afterwards, output $k$ lines. The $i$ -th line should contain two integers $l_i$ and $r_i$ ( $1 \leq l_i \leq r_i \leq n$ ) — the left and right indices for the $i$ -th operation.

You can output "YES" and "NO" in any case (for example, strings "yEs", "yes" and "Yes" will be recognized as a positive response).

If there are multiple possible sequences of operations, you may output any of them.

输入输出样例

输入#1

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

输出#1

YES
2
5 8
1 6
YES
2
1 4
3 6
NO
NO
YES
0

说明/提示

In the first test case, we can perform the following operations: $$$$[1,2,4,3,1,2,1,1] \xrightarrow[l=5,,r=8]{} [1,2,4,3,1,1,2,1] \xrightarrow[l=1,,r=6]{} [1,1,3,4,2,1,2,1]. $$

In the second test case, we can perform the following operations: $$ [1,2,3,1,3,2,3] \xrightarrow[l=1,,r=4]{} [1,3,2,1,3,2,3] \xrightarrow[l=3,,r=6]{} [1,3,2,3,1,2,3]. $$

It can be proven that it is impossible to turn $a$ into $b$ $$ in the third and fourth test cases.

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