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.