## Description

A permutation of the numbers 1, ..., N is a rearrangment of these numbers. For example
`2  4  5  1  7  6  3  8 `
is a permutation of 1,2, ..., 8. Of course,
`1  2  3  4  5  6  7  8 `
is also a permutation of 1, 2, ..., 8.

Associated with each permutation of N is a special sequence of positive integers of length N called its inversion sequence. The ith element of this sequence is the number of numbers j that are strictly less than i and appear to the right of i in this permutation. For the permutation
`2  4  5  1  7  6  3  8 `
the inversion sequence is
`0  1  0  2  2  1  2  0 `
The 2nd element is 1 because 1 is strictly less than 2 and it appears to the right of 2 in this permutation. Similarly, the 5th element is 2 since 1 and 3 are strictly less than 5 but appear to the right of 5 in this permutation and so on.

As another example, the inversion sequence of the permutation
`8  7  6  5  4  3  2  1 `
is
`0  1  2  3  4  5  6  7 `
In this problem, you will be given the inversion sequence of some permutation. Your task is to reconstruct the permutation from this sequence.

## Input

The input contains multiple test cases. For each test case, the first line consists of a single integer N. The following line contains N integers, describing an inversion sequence.

You may assume that N <= 100000. You may further assume that in at least 50% of the inputs N <= 8000.

## Output

For each test case, a single line with N integers describing a permutation of 1, 2, ..., N whose inversion sequence is the given input sequence.

## Sample Input

```8
0 1 0 2 2 1 2 0
8
0 1 2 3 4 5 6 7```

## Sample Output

```2 4 5 1 7 6 3 8
8 7 6 5 4 3 2 1```