You are given a sequence D_1, D_2, ..., D_N of length N.
The values of D_i are all distinct.
Does a tree with N vertices that satisfies the following conditions exist?
 - The vertices are numbered 1,2,..., N.
 - The edges are numbered 1,2,..., N-1, and Edge i connects Vertex u_i and v_i.
 - For each vertex i, the sum of the distances from i to the other vertices is D_i, assuming that the length of each edge is 1.
If such a tree exists, construct one such tree.

-----Constraints-----
 - 2 \leq N \leq 100000
 - 1 \leq D_i \leq 10^{12}
 - D_i are all distinct.

-----Input-----
Input is given from Standard Input in the following format:
N
D_1
D_2
:
D_N

-----Output-----
If a tree with n vertices that satisfies the conditions does not exist, print -1.
If a tree with n vertices that satisfies the conditions exist, print n-1 lines.
The i-th line should contain u_i and v_i with a space in between.
If there are multiple trees that satisfy the conditions, any such tree will be accepted.

-----Sample Input-----
7
10
15
13
18
11
14
19

-----Sample Output-----
1 2
1 3
1 5
3 4
5 6
6 7

The tree shown below satisfies the conditions.

```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\n\nN = int(input())\nD = [None] + [int(input()) for _ in range(N)]\n\nparent = [None] * (N+1)\nsize = [None] + [1] * N # 部分木の頂点数、自分を含む\nd_to_i = {d:i for i,d in enumerate(D)}\nD_desc = sorted(D[1:],reverse=True)\nD_subtree = [0] * (N+1)\nedges = []\n\nbl = True\nfor d in D_desc[:-1]:\n    i = d_to_i[d]\n    d_parent = d - N + 2*size[i]\n    if d_parent not in d_to_i:\n        bl = False\n        break\n    p = d_to_i[d_parent]\n    edges.append('{} {}'.format(i,p))\n    parent[i] = p\n    size[p] += size[i]\n    D_subtree[p] += D_subtree[i] + size[i]\n\nroot = d_to_i[D_desc[-1]]\nbl &= (D_subtree[root] == D[root])\n\nif bl:\n    print('\\n'.join(edges))\nelse:\n    print(-1)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13537