For $N$ integers $0, 1, \dots, N-1$, a transformation sequence $T$ maps $i$ to $T_i$, where $T_i \in \{0, 1, \dots, N-1\}$ and $\bigcup_{i=0}^{N-1} \{T_i\} = \{0, 1, \dots, N-1\}$. For any $x, y \in \{0, 1, \dots, N-1\}$, the distance between $x$ and $y$ is defined as $D(x, y) = \min\{|x-y|, N-|x-y|\}$. Given the distance $D(i, T_i)$ for each $i$, you need to find a transformation sequence $T$ that satisfies the requirements. If there are multiple such sequences, output the one that is lexicographically smallest.

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

Input

The first line contains an integer $N$, representing the length of the sequence. The next line contains $N$ integers $D_i$, where $D_i$ represents the distance between $i$ and $T_i$.

Output

If at least one valid transformation sequence $T$ exists, output a single line containing $N$ integers, representing the lexicographically smallest $T$ you calculated; otherwise, output "No Answer" (without quotes). Note: Adjacent numbers in the output should be separated by a single space, and there should be no trailing spaces at the end of the line.

Constraints

20% of the data: $N \le 50$; 60% of the data: $N \le 500$; 100% of the data: $N \le 10000$.

Examples

Input 1

5
1 1 2 2 1

Output 1

1 2 4 0 3