Find the Permutation

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A permutation of the numbers $1, ..., N$ is a rearrangment of these numbers. For example $$2 \quad 4 \quad 5 \quad 1 \quad 7 \quad 6 \quad 3 \quad 8$$ is a permutation of $1,2, ..., 8$. Of course, $$1 \quad 2 \quad 3 \quad 4 \quad 5 \quad 6 \quad 7 \quad 8$$ 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 $$2 \quad 4 \quad 5 \quad 1 \quad 7 \quad 6 \quad 3 \quad 8$$ the inversion sequence is $$0 \quad 1 \quad 0 \quad 2 \quad 2 \quad 1 \quad 2 \quad 0$$ The $2^{nd}$ element is $1$ because $1$ is strictly less than $2$ and it appears to the right of $2$ in this permutation. Similarly, the $5^{th}$ 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 $$8 \quad 7 \quad 6 \quad 5 \quad 4 \quad 3 \quad 2 \quad 1$$ is $$0 \quad 1 \quad 2 \quad 3 \quad 4 \quad 5 \quad 6 \quad 7$$ 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 first line consists of a single integer $N$. The following line contains $N$ integers, describing an inversion sequence. ###Output: A single line with N integers describing a permutation of $1, 2, ..., N$ whose inversion sequence is the given input sequence. ###Constraints: - $1 \leq N \leq 100000$. - You may further assume that in at least $50 \%$ of the inputs $1 \leq N \leq 8000$. ###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