National Olympiad in Informatics, China, 2009

For $N$ integers $0,1,\dots ,N-1$, a transformed sequence $T$ can change $i$ to $T_i$, where $T_i\in \{0,1,\dots ,N-1\}$ and $\bigcup _{i=0}^{N-1}\{T_i\}=\{0,1,\dots ,N-1\}$. $\mathrm{\forall }x,y\in \{0,1,\dots ,N-1\}$, define the distance between $x$ and $y$ to be $D(x,y)=min\{|x-y|,N-|x-y|\}$. Given the distance $D(i,T_i)$ between each $i$ and $T_i$, you must determine a transformed sequence $T$ that satisfies the requirements. If many sequences satisfy the requirements, then output the lexicographically smallest one.

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

Input Specification

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

Output Specification

If there exists at least one transformed sequence $T$, then output one line containing $N$ integers, representing the lexicographically smallest transformed sequence $T$. Otherwise, output No Answer.

Note: Pairs of adjacent numbers in the output must be separated by a single space, and there cannot be trailing spaces.

Sample Input

5
1 1 2 2 1

Sample Output

1 2 4 0 3

Constraints

For 20% of the test data, $N\le 50$.
For 60% of the test data, $N\le 500$.
For 100% of the test data, $N\le 10000$.

Problem translated to English by Alex.