Transformed Sequence

For $N$ integers $0, 1, \ldots, N-1$, a transformed sequence $T$ changes each $i$ to $T_i$, where $T_i \in \{0, 1, \ldots, N-1\}$ and $\bigcup_{i=0}^{N-1} \{T_i\} = \{0, 1, \ldots, N-1\}$. For all $x, y \in \{0, 1, \ldots, N-1\}$, the distance between $x$ and $y$ is $D(x, y) = \min\{|x - y|, N - |x - y|\}$. Given the distance $D(i, T_i)$ for each $i$, find a transformed sequence $T$ that satisfies these requirements. If several sequences satisfy them, output the lexicographically smallest one.

Note: For two transformed sequences $S$ and $T$, $S$ is lexicographically smaller than $T$ if there exists a $p < N$ such that $S_i = T_i$ for $i = 0, 1, \ldots, p-1$ and $S_p < T_p$.

The first line contains a single integer $N$, the length of the sequence. The next line contains $N$ integers $D_i$, where $D_i$ is the distance between $i$ and $T_i$.

If at least one transformed sequence $T$ exists, print one line with $N$ integers, the lexicographically smallest $T$. Otherwise, print No Answer. Separate adjacent numbers with a single space, and do not leave a trailing space.

$N \le 10000$