CF1998B Minimize Equal Sum Subarrays

It is known that [Farmer John likes Permutations](https://usaco.org/index.php?page=viewproblem2&cpid=1421), but I like them too! — Sun Tzu, The Art of Constructing Permutations You are given a permutation $ ^{\text{∗}} $ $ p $ of length $ n $ . Find a permutation $ q $ of length $ n $ that minimizes the number of pairs ( $ i, j $ ) ( $ 1 \leq i \leq j \leq n $ ) such that $ p_i + p_{i+1} + \ldots + p_j = q_i + q_{i+1} + \ldots + q_j $ . $ ^{\text{∗}} $ A permutation of length $ n $ is an array consisting of $ n $ distinct integers from $ 1 $ to $ n $ in arbitrary order. For example, $ [2,3,1,5,4] $ is a permutation, but $ [1,2,2] $ is not a permutation ( $ 2 $ appears twice in the array), and $ [1,3,4] $ is also not a permutation ( $ n=3 $ but there is $ 4 $ in the array).

The first line contains $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. The first line of each test case contains $ n $ ( $ 1 \leq n \leq 2 \cdot 10^5 $ ). The following line contains $ n $ space-separated integers $ p_1, p_2, \ldots, p_n $ ( $ 1 \leq p_i \leq n $ ) — denoting the permutation $ p $ of length $ n $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output one line containing any permutation of length $ n $ (the permutation $ q $ ) such that $ q $ minimizes the number of pairs.

For the first test, there exists only one pair ( $ i, j $ ) ( $ 1 \leq i \leq j \leq n $ ) such that $ p_i + p_{i+1} + \ldots + p_j = q_i + q_{i+1} + \ldots + q_j $ , which is ( $ 1, 2 $ ). It can be proven that no such $ q $ exists for which there are no pairs.