A. Special Permutation
constructive algorithms; probabilities
You are given one integer \(n\) (\(n > 1\)).Recall that 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 of length \(5\), 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).Your task is to find a permutation \(p\) of length \(n\) that there is no index \(i\) (\(1 \le i \le n\)) such that \(p_i = i\) (so, for all \(i\) from \(1\) to \(n\) the condition \(p_i \ne i\) should be satisfied).You have to answer \(t\) independent test cases.If there are several answers, you can print any. It can be proven that the answer exists for each \(n > 1\).
The first line of the input contains one integer \(t\) (\(1 \le t \le 100\)) — the number of test cases. Then \(t\) test cases follow.The only line of the test case contains one integer \(n\) (\(2 \le n \le 100\)) — the length of the permutation you have to find.
For each test case, print \(n\) distinct integers \(p_1, p_2, \ldots, p_n\) — a permutation that there is no index \(i\) (\(1 \le i \le n\)) such that \(p_i = i\) (so, for all \(i\) from \(1\) to \(n\) the condition \(p_i \ne i\) should be satisfied).If there are several answers, you can print any. It can be proven that the answer exists for each \(n > 1\).