Codeforces Round 771 (Div. 2) |
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constructive algorithms

greedy

math

*800

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A. Reverse

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a permutation $$$p_1, p_2, \ldots, p_n$$$ of length $$$n$$$. You have to choose two integers $$$l,r$$$ ($$$1 \le l \le r \le n$$$) and reverse the subsegment $$$[l,r]$$$ of the permutation. The permutation will become $$$p_1,p_2, \dots, p_{l-1},p_r,p_{r-1}, \dots, p_l,p_{r+1},p_{r+2}, \dots ,p_n$$$.

Find the lexicographically smallest permutation that can be obtained by performing exactly one reverse operation on the initial permutation.

Note that for two distinct permutations of equal length $$$a$$$ and $$$b$$$, $$$a$$$ is lexicographically smaller than $$$b$$$ if at the first position they differ, $$$a$$$ has the smaller element.

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 a single integer $$$t$$$ ($$$1 \le t \le 500$$$) — the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 500$$$) — the length of the permutation.

The second line of each test case contains $$$n$$$ integers $$$p_1, p_2, \dots, p_n$$$ ($$$1 \le p_i \le n$$$) — the elements of the permutation.

Output

For each test case print the lexicographically smallest permutation you can obtain.

Example

Input

41132 1 341 4 2 351 2 3 4 5

Output

1 1 2 3 1 2 4 3 1 2 3 4 5

Note

In the first test case, the permutation has length $$$1$$$, so the only possible segment is $$$[1,1]$$$. The resulting permutation is $$$[1]$$$.

In the second test case, we can obtain the identity permutation by reversing the segment $$$[1,2]$$$. The resulting permutation is $$$[1,2,3]$$$.

In the third test case, the best possible segment is $$$[2,3]$$$. The resulting permutation is $$$[1,2,4,3]$$$.

In the fourth test case, there is no lexicographically smaller permutation, so we can leave it unchanged by choosing the segment $$$[1,1]$$$. The resulting permutation is $$$[1,2,3,4,5]$$$.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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