Restore Permutation

现在有一个从$1$到$n$的一个全排列,但是你不知道这个排列到底是什么,但是你有一个$sum[i]$,其中$sum[i]$表示$\sum_{j=1}^{i-1}(a_j<a_i)?a_j:0$,现在给你$sum$数组,让你求出这个排列$a$

An 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.

The 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 $ .

Print $ n $ integers $ p_{1}, p_{2}, \ldots, p_{n} $ — the elements of the restored permutation. We can show that the answer is always unique.

3
0 0 0

3 2 1

2
0 1

1 2

5
0 1 1 1 10

1 4 3 2 5

In 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 $ .