codeforces#P1711A. Perfect Permutation
Perfect Permutation
Description
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.
Input
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 $10^5$.
Output
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.
Samples
2
1
4
1
2 1 4 3
Note
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.