D. Restore Permutationtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputAn array of integers p_{1},p_{2}, \ldots,p_{n} is called a permutation if it contains each number from 1 to n exactly once. For example, the following arrays are permutations: [3,1,2], [1], [1,2,3,4,5] and [4,3,1,2]. The following arrays are not permutations: [2], [1,1], [2,3,4].There is a hidden permutation of length n.For each index i, you are given s_{i}, which equals to the sum of all p_{j} such that j < i and p_{j} < p_{i}. In other words, s_i is the sum of elements before the i-th element that are smaller than the i-th element.Your task is to restore the permutation.InputThe first line contains a single integer n (1 \le n \le 2 \cdot 10^{5}) — the size of the permutation.The second line contains n integers s_{1}, s_{2}, \ldots, s_{n} (0 \le s_{i} \le \frac{n(n-1)}{2}).It is guaranteed that the array s corresponds to a valid permutation of length n.OutputPrint n integers p_{1}, p_{2}, \ldots, p_{n} — the elements of the restored permutation. We can show that the answer is always unique.ExamplesInput
3
0 0 0
Output
3 2 1
Input
2
0 1
Output
1 2
Input
5
0 1 1 1 10
Output
1 4 3 2 5
NoteIn the first example for each i there is no index j satisfying both conditions, hence s_i are always 0.In the second example for i = 2 it happens that j = 1 satisfies the conditions, so s_2 = p_1.In the third example for i = 2, 3, 4 only j = 1 satisfies the conditions, so s_2 = s_3 = s_4 = 1. For i = 5 all j = 1, 2, 3, 4 are possible, so s_5 = p_1 + p_2 + p_3 + p_4 = 10.
3
0 0 0

3 2 1 
['binary search', 'data structures', 'greedy', 'implementation', '*1900']