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A. Perfect Permutation

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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).

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.

Example

Input

214

Output

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.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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