Codeforces Round 794 (Div. 1) |
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Finished |

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constructive algorithms

dfs and similar

dsu

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D1. Permutation Weight (Easy Version)

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThis is an easy version of the problem. The difference between the easy and hard versions is that in this version, you can output any permutation with the smallest weight.

You are given a permutation $$$p_1, p_2, \ldots, p_n$$$ of integers from $$$1$$$ to $$$n$$$.

Let's define the weight of the permutation $$$q_1, q_2, \ldots, q_n$$$ of integers from $$$1$$$ to $$$n$$$ as $$$$$$|q_1 - p_{q_{2}}| + |q_2 - p_{q_{3}}| + \ldots + |q_{n-1} - p_{q_{n}}| + |q_n - p_{q_{1}}|$$$$$$

You want your permutation to be as lightweight as possible. Find any permutation $$$q$$$ with the smallest possible weight.

Input

The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 200$$$) — the size of the permutation.

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

The sum of $$$n$$$ over all test cases doesn't exceed $$$400$$$.

Output

For each test case, output $$$n$$$ integers $$$q_1, q_2, \ldots, q_n$$$ ($$$1 \le q_i \le n$$$, all $$$q_i$$$ are distinct) — one of the permutations with the smallest weight.

Example

Input

322 142 3 1 455 4 3 2 1

Output

1 2 1 3 4 2 1 4 2 3 5

Note

In the first test case, there are two permutations of length $$$2$$$: $$$(1, 2)$$$ and $$$(2, 1)$$$. Permutation $$$(1, 2)$$$ has weight $$$|1 - p_2| + |2 - p_1| = 0$$$, and permutation $$$(2, 1)$$$ has the same weight: $$$|2 - p_1| + |1 - p_2| = 0$$$. You can output any of these permutations in this version.

In the second test case, the weight of the permutation $$$(1, 3, 4, 2)$$$ is $$$|1 - p_3| + |3 - p_4| + |4 - p_2| + |2 - p_1| = |1 - 1| + |3 - 4| + |4 - 3| + |2 - 2| = 2$$$. There are no permutations with smaller weights.

In the third test case, the weight of the permutation $$$(1, 4, 2, 3, 5)$$$ is $$$|1 - p_4| + |4 - p_2| + |2 - p_3| + |3 - p_5| + |5 - p_1| = |1 - 2| + |4 - 4| + |2 - 3| + |3 - 1| + |5 - 5| = 4$$$. There are no permutations with smaller weights.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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