CF1208D.Restore Permutation

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 $j \lt i$ and $p_{j} \lt p_{i}$. 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.

一个整数数组 $p_{1},p_{2}, \ldots,p_{n}$ 被称为排列，当且仅当它恰好包含从 $1$ 到 $n$ 的每个整数各一次。例如，以下数组均为排列：$[3,1,2]$、$[1]$、$[1,2,3,4,5]$ 和 $[4,3,1,2]$；而以下数组不是排列：$[2]$、$[1,1]$、$[2,3,4]$。

现存在一个长度为 $n$ 的隐藏排列。

对每个下标 $i$，你将获得 $s_{i}$，其值等于所有满足 $j \lt i$ 且 $p_{j} \lt p_{i}$ 的 $p_{j}$ 之和。换言之，$s_i$ 是第 $i$ 个元素之前所有比它小的元素之和。

你的任务是还原出该排列。

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 $n$.

第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^{5}$）—— 表示排列的长度。

第二行包含 $n$ 个整数 $s_{1}, s_{2}, \ldots, s_{n}$（$0 \le s_{i} \le \frac{n(n-1)}{2}$）。

保证数组 $s$ 对应一个长度为 $n$ 的合法排列。

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.

输出 $n$ 个整数 $p_{1}, p_{2}, \ldots, p_{n}$ —— 恢复得到的排列的各个元素。可以证明答案总是唯一的。

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 $s_5 = p_1 + p_2 + p_3 + p_4 = 10$.

在第一个例子中，对每个 $i$，都不存在满足两个条件的索引 $j$，因此所有 $s_i$ 恒为 $0$。

在第二个例子中，当 $i = 2$ 时，$j = 1$ 满足条件，故 $s_2 = p_1$。

在第三个例子中，当 $i = 2, 3, 4$ 时，仅 $j = 1$ 满足条件，因此 $s_2 = s_3 = s_4 = 1$；当 $i = 5$ 时，所有 $j = 1, 2, 3, 4$ 均满足条件，故 $s_5 = p_1 + p_2 + p_3 + p_4 = 10$。