[Solution] Perfect Permutation Codeforces Solution

A. Perfect Permutation

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given a positive integer 𝑛$n$.

The weight of a permutation 𝑝1,𝑝2,…,𝑝𝑛$p_1,p_2,\dots ,p_n$ is the number of indices 1≤𝑖≤𝑛$1\le i\le n$ such that 𝑖$i$ divides 𝑝𝑖$p_i$. Find a permutation 𝑝1,𝑝2,…,𝑝𝑛$p_1,p_2,\dots ,p_n$ with the minimum possible weight (among all permutations of length 𝑛$n$).

A permutation is an array consisting of 𝑛$n$ distinct integers from 1$1$ to 𝑛$n$ in arbitrary order. For example, [2,3,1,5,4]$[2,3,1,5,4]$ is a permutation, but [1,2,2]$[1,2,2]$ is not a permutation (2$2$ appears twice in the array) and [1,3,4]$[1,3,4]$ is also not a permutation (𝑛=3$n=3$ but there is 4$4$ in the array).

Input

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Each test contains multiple test cases. The first line contains the number of test cases 𝑡$t$ (1≤𝑡≤104$1\le t\le {10}^4$). The description of the test cases follows.

The only line of each test case contains a single integer 𝑛$n$ (1≤𝑛≤105$1\le n\le {10}^5$) — the length of permutation.

It is guaranteed that the sum of 𝑛$n$ over all test cases does not exceed 105${10}^5$.

Output

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For each test case, print a line containing 𝑛$n$ integers 𝑝1,𝑝2,…,𝑝𝑛$p_1,p_2,\dots ,p_n$ so that the permutation 𝑝$p$ has the minimum possible weight.

If there are several possible answers, you can print any of them.