Permutation

Time limit0.5sMemory limit512 MB

Summary

Reconstruct a permutation of 1..N from A[i], the count of larger elements appearing before i, typically using a Fenwick tree or BIT with binary search.

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

Problem

A permutation contains each integer from 1 through N exactly once. For a value i, define A[i] as the number of elements greater than i that appear before i in the permutation. Given all values A[i], reconstruct the original permutation.

Input

The first line contains the length N of the permutation (1 ≤ N ≤ 100,000). The next N lines contain A[i] for i=1,2,...,N in order, one value per line.

Output

Print the original permutation in order over N lines. The k-th line must contain the k-th element of the permutation.

Examples1

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