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.


-----Input-----

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 $n$.


-----Output-----

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.


-----Examples-----
Input
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



-----Note-----

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

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'from operator import add\n\nclass Stree:\n    def __init__(self, f, n, default, init_data):\n        self.ln = 2**(n-1).bit_length()\n        self.data = [default] * (self.ln * 2)\n        self.f = f\n        for i, d in init_data.items():\n            self.data[self.ln + i] = d\n        for j in range(self.ln - 1, 0, -1):\n            self.data[j] = f(self.data[j*2], self.data[j*2+1])\n\n    def update(self, i, a):\n        p = self.ln + i\n        self.data[p] = a\n        while p > 1:\n            p = p // 2\n            self.data[p] = self.f(self.data[p*2], self.data[p*2+1])\n\n    def get(self, i, j):\n        def _get(l, r, p):\n            if i <= l and j >= r:\n                return self.data[p]\n            else:\n                m = (l+r)//2\n                if j <= m:\n                    return _get(l, m, p*2)\n                elif i >= m:\n                    return _get(m, r, p*2+1)\n                else:\n                    return self.f(_get(l, m, p*2), _get(m, r, p*2+1))\n        return _get(0, self.ln, 1)\n\n    def find_value(self, v):\n        def _find_value(l, r, p, v):\n            if r == l+1:\n                return l\n            elif self.data[p*2] <= v:\n                return _find_value((l+r)//2, r, p*2+1, v - self.data[p*2])\n            else:\n                return _find_value(l, (l+r)//2, p*2, v)\n        return _find_value(0, self.ln, 1, v)\n\n\ndef main():\n    n = int(input())\n    sums = {i:i for i in range(n+1)}\n    stree = Stree(add, n+1, 0, sums)\n    ss = list(map(int, input().split()))\n    ss.reverse()\n    pp = []\n    for s in ss:\n        sval = stree.find_value(s)\n        pp.append(sval)\n        stree.update(sval,0)\n    print(*(reversed(pp)))\n\ndef __starting_point():\n    main()\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 17231