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

Source