Permutation Transformation

Given N integers \(0, 1, \cdots, N-1\), a transformation sequence \(T\) maps each integer \(i\) to \(T_i\). The sequence \(T\) must satisfy \(\{T_0, T_1, \cdots, T_{N-1}\} = \{0, 1, \cdots, N-1\}\). For any \(x, y \in \{0, 1, \cdots, N-1\}\), the distance between \(x\) and \(y\) is defined as \[ D(x,y)=\min\{|x-y|,\,N-|x-y|\} \] You are given an array of \(N\) integers where the \(i\)-th integer represents \(D(i, T_i)\). Your task is to determine a transformation sequence \(T\) that satisfies these distances. If multiple solutions exist, output the lexicographically smallest one.

inputFormat

The first line contains an integer \(N\) representing the number of integers. The second line contains \(N\) space-separated integers \(d_0, d_1, \ldots, d_{N-1}\) where \(d_i = D(i, T_i)\).

outputFormat

Print a single line containing \(N\) space-separated integers representing the transformation sequence \(T\). If a valid sequence exists, it will be unique under the lexicographical minimality requirement.

sample

3
0 1 1

0 2 1