CF1711A Perfect Permutation

You are given a positive integer $ n $ . The weight of a permutation $ p_1, p_2, \ldots, p_n $ is the number of indices $ 1\le i\le n $ such that $ i $ divides $ p_i $ . Find a permutation $ p_1,p_2,\dots, p_n $ with the minimum possible weight (among all permutations of length $ n $ ). A permutation 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).

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \leq t \leq 10^4 $ ). The description of the test cases follows. The only line of each test case contains a single integer $ n $ ( $ 1 \leq n \leq 10^5 $ ) — the length of permutation. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^5 $ .

For each test case, print a line containing $ n $ integers $ p_1, p_2,\dots, p_n $ so that the permutation $ p $ has the minimum possible weight. If there are several possible answers, you can print any of them.

In the first test case, the only valid permutation is $ p=[1] $ . Its weight is $ 1 $ . In the second test case, one possible answer is the permutation $ p=[2,1,4,3] $ . One can check that $ 1 $ divides $ p_1 $ and $ i $ does not divide $ p_i $ for $ i=2,3,4 $ , so the weight of this permutation is $ 1 $ . It is impossible to find a permutation of length $ 4 $ with a strictly smaller weight.