Lost Lineup

Source: Kattis

Version: Phuoc Hung OJ Extended

Problem

Person 1 (Jimmy) is first. For each person $i\ge2$, $d_i$ is the number of people between that person and Jimmy. Hence its 1-based position is $d_i+2$, equivalently ans[d_i+1]=i in a 0-based array. The distances form a permutation of $0,\ldots,n-2$.

Input

The first line contains $n$. If $n>1$, the next line contains $d_2,\ldots,d_n$.

Output

Print the reconstructed lineup.

Subtask

Subtask 1 (20 points): $1\le n\le10$.

Subtask 2 (30 points): $1\le n\le50$.

Subtask 3 (50 points): $1\le n\le100$.

Example

Input

4
1 2 0

Output

1 4 2 3

Explanation

Distance 0 is immediately behind Jimmy; the other distances determine the remaining positions.