Permutation Restoration

Time limit0.55sMemory limit128 MB

Summary

Given the inversion sequence of a permutation of 1..N, reconstruct the original permutation using an efficient data structure.

Level: Medium6 of 10
Topics: Segment tree, Binary search, Greedy, Array
Solved: No attempts yet

Problem

There is a permutation containing each integer from 1 to N exactly once. For each value i, the i-th value of its inversion sequence is the number of values smaller than i that appear to the right of i in the permutation.

For example, the permutation 2 4 5 1 7 6 3 8 has inversion sequence 0 1 0 2 2 1 2 0.

Given an inversion sequence, write a program that restores the corresponding permutation.

Input

The first line contains the size N of the permutation. (1 <= N <= 100,000)

The second line contains the inversion sequence for the values 1, 2, ..., N, separated by spaces.

Output

Print the permutation corresponding to the given inversion sequence on one line, with values separated by spaces.

Examples2

Example 1
Input
```
8
0 1 0 2 2 1 2 0
```
Expected output
```
2 4 5 1 7 6 3 8
```
Example 2
Input
```
8
0 1 2 3 4 5 6 7
```
Expected output
```
8 7 6 5 4 3 2 1
```