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 = "\ndef solve():\n    # N = int(raw_input())\n    # D = [int(raw_input()) for i in range(N)]\n    N = int(input())\n    D = [int(input()) for i in range(N)]\n    if sum(D) % 2 > 0:\n        print ('-1')\n        return\n    Di = sorted([(di, i) for i, di in enumerate(D)], key = lambda x : x[0], reverse = True)\n    d_to_i = {dd:i for dd, i in Di}\n    # child = [[] for i in range(N)]\n    ans = []\n    n_child = [1] * N\n    d_child = [0] * N\n    for valD, node in Di:\n        valD_par = valD - N + 2 * n_child[node]\n        if valD_par in list(d_to_i.keys()):\n            node_par = d_to_i[valD_par]\n            # child[node].append(node_par) ##\n            # child[node_par].append(node)\n            ans.append((node_par + 1, node + 1))\n            n_child[node_par] += n_child[node]\n            d_child[node_par] += n_child[node] + d_child[node]\n            if n_child[node_par] == N:\n                break\n        else:\n            print ('-1')\n            return\n    # check if Di satisfied or not\n    d_min, i_min = Di[-1]\n    if d_child[i_min] != d_min:\n        print ('-1')\n        return\n    # for i in range(N):\n    #     for j in child[i]:\n    #         print str(i + 1) + ' ' + str(j + 1)\n    for i,j in ans:\n        print((str(i) + ' ' + str(j)))\n\ndef __starting_point():\n    solve()\n\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14403