Problem 2: Find the
Permutation, *(Tanmoy Chakraborty, Indraneel Mukherjee, CMI)*

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 *i*th 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 format

The first line consists of a single integer *N*. The
following line contains *N* integers, describing an inversion
sequence.

Output format

A single line with *N* integers describing a permutation of
1, 2, ..., *N* whose inversion sequence is the given input
sequence.

Test Data:

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

Example:

Here are sample inputs and outputs corresponding to the example discussed above.

Sample Input 1

8 0 1 0 2 2 1 2 0

Sample Output 1

2 4 5 1 7 6 3 8

Sample Input 2

8 0 1 2 3 4 5 6 7

Sample Output 2

8 7 6 5 4 3 2 1

Copyright (c) IARCS 2003-2018; Last Updated: 05 Jul 2005