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 = 'import sys\ninput = sys.stdin.readline\nclass SegTree(object):\n\t"""docstring for SegTree"""\n\tdef __init__(self, n, arr):\n\t\tself.n = n\n\t\tself.arr = arr\n\t\tself.tree = [0 for i in range(2*n)]\n\n\tdef construct(self): # Construction\n\t\tfor i in range(self.n):\n\t\t\tself.tree[n+i] = self.arr[i]\n\t\tfor i in range(n-1,0,-1):\n\t\t\tself.tree[i] = self.function(self.tree[2*i],self.tree[2*i+1])\n\n\tdef update(self,index,value):\n\t\tstart = index+self.n\n\t\tself.tree[start] = value\n\t\twhile start>0:\n\t\t\tstart = start//2\n\t\t\tself.tree[start] = self.function(self.tree[2*start],self.tree[2*start+1])\n\n\tdef calc(self,low,high): # 0-indexed\n\t\tlow+=self.n\n\t\thigh+=self.n\n\t\tans = 0 # Needs to initialised\n\t\twhile low<high:\n\t\t\tif low%2:\n\t\t\t\tans = self.function(ans, self.tree[low])\n\t\t\t\tlow += 1\n\t\t\tif high%2:\n\t\t\t\thigh -= 1\n\t\t\t\tans = self.function(ans, self.tree[high])\n\t\t\tlow = low//2\n\t\t\thigh = high//2\n\t\treturn ans\n\t\n\tdef function(self,a,b): # Function used to construct Segment Tree\n\t\treturn a + b\n\n\ndef find(num):\n\tlow = 0\n\thigh = n-1\n\twhile low<high:\n\t\tmid = (low+high)//2\n\t\tif st.calc(0,mid+1)>num:\n\t\t\thigh = mid - 1\n\t\telse:\n\t\t\tlow = mid + 1\n\tif st.calc(0,low+1)>num:\n\t\treturn low\n\telse:\n\t\treturn low + 1\n\n\n\nn = int(input())\na = list(map(int,input().split()))\narr = [i for i in range(1,n+1)]\nst = SegTree(n,arr)\nst.construct()\nans = [-1]*n\nfor i in range(n-1,-1,-1):\n\tind = find(a[i])\n\t# print (a[i],ind,arr)\n\tans[i] = arr[ind]\n\tst.update(ind,0)\nprint(*ans)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 16805