Farmer John has an array \(A\) containing \(N\) integers
(\(1 \leq N \leq 5 \cdot 10^5, 1 \leq A_i \leq N\)). He picks his favorite index
\(j\) and take out a sheet of paper with only \(A_j\) written on it. He can then
perform the following operation some number of times:

• Cyclically shift all elements in \(A\) one spot to the left or one spot to the right. Then, write down \(A_j\) on a piece of paper.

Let \(S\) denote the set of distinct integers that occur in \(A\). Farmer John
wonders what the minimum number of operations he must perform is so that the
paper contains all integers that appear in \(S\).

Since it is unclear what FJ's favorite index is, output the answer for all
possible favorite indices \(1 \leq j \leq N\). Note for each index, \(A\) is reset
to its original form before performing any operations.

Problem credits: Chongtian Ma

SCORING

• Inputs 3-5: \(N\le 500\)
• Inputs 6-8: \(N\le 10^4\)
• Inputs 9-17: No additional constraints.

Problem credits: Chongtian Ma

The first line contains \(N\).

The following line contains \(A_1, A_2, \ldots, A_N\).

Output \(N\) space-separated integers, where the \(i\)'th integer is the answer for
his favorite index \(j = i\).

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