Codeforces Round 965 (Div. 2) |
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Finished |
You are given a permutation$$$^{\text{∗}}$$$ $$$p$$$ of length $$$n$$$.
Find a permutation $$$q$$$ of length $$$n$$$ that minimizes the number of pairs ($$$i, j$$$) ($$$1 \leq i \leq j \leq n$$$) such that $$$p_i + p_{i+1} + \ldots + p_j = q_i + q_{i+1} + \ldots + q_j$$$.
$$$^{\text{∗}}$$$A permutation of length $$$n$$$ 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).
The first line contains $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.
The first line of each test case contains $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$).
The following line contains $$$n$$$ space-separated integers $$$p_1, p_2, \ldots, p_n$$$ ($$$1 \leq p_i \leq n$$$) — denoting the permutation $$$p$$$ of length $$$n$$$.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
For each test case, output one line containing any permutation of length $$$n$$$ (the permutation $$$q$$$) such that $$$q$$$ minimizes the number of pairs.
321 251 2 3 4 574 7 5 1 2 6 3
2 1 3 5 4 2 1 6 2 1 4 7 3 5
For the first test, there exists only one pair ($$$i, j$$$) ($$$1 \leq i \leq j \leq n$$$) such that $$$p_i + p_{i+1} + \ldots + p_j = q_i + q_{i+1} + \ldots + q_j$$$, which is ($$$1, 2$$$). It can be proven that no such $$$q$$$ exists for which there are no pairs.
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