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 = 'def sumsegtree(l,seg,st,en,x):\n    if st==en:\n        seg[x]=l[st]\n    else:\n        mid=(st+en)>>1\n        sumsegtree(l,seg,st,mid,2*x)\n        sumsegtree(l,seg,mid+1,en,2*x+1)\n        seg[x]=seg[2*x]+seg[2*x+1]\n \ndef query(seg,st,en,val,x):\n    if st==en:\n        return seg[x]\n    mid=(st+en)>>1\n    if seg[2*x]>=val:\n        return query(seg,st,mid,val,2*x)\n    return query(seg,mid+1,en,val-seg[2*x],2*x+1)\n \ndef upd(seg,st,en,ind,val,x):\n    if st==en:\n        seg[x]=val\n        return\n    mid=(st+en)>>1\n    if mid>=ind:\n        upd(seg,st,mid,ind,val,2*x)\n    else:\n        upd(seg,mid+1,en,ind,val,2*x+1)\n    seg[x]=seg[2*x]+seg[2*x+1]\n \nn=int(input())\nl=list(map(int,range(1,n+1)))\ns=[0]*n\np=list(map(int,input().split()))\n \n \nseg=["#"]*(n<<2)\nsumsegtree(l,seg,0,len(l)-1,1)\n \nfor i in range(len(p)-1,-1,-1):\n    s[i]=query(seg,1,n,p[i]+1,1)\n    upd(seg,1,n,s[i],0,1)\n \nprint (*s)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13677