CF1698F Equal Reversal

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.

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 $ .

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.

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.