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 = 'N = int(input())\nsrc = [int(input()) for i in range(N)]\nidx = {a:i for i,a in enumerate(src)}\n\nsize = [1] * N\nss = list(sorted(src))\n\nes = []\ngr = [[] for i in range(N)]\nwhile len(ss) > 1:\n    a = ss.pop()\n    k = size[idx[a]]\n    b = a + 2*k - N\n    if b == a or b not in idx:\n        print(-1)\n        return\n    size[idx[b]] += k\n    ai,bi = idx[a],idx[b]\n    es.append((ai,bi))\n    gr[ai].append(bi)\n    gr[bi].append(ai)\n\nfrom collections import deque\ndist = [N] * N\ndist[idx[ss[0]]] = 0\nq = deque([idx[ss[0]]])\nwhile q:\n    v = q.popleft()\n    for to in gr[v]:\n        if dist[to] < N: continue\n        q.append(to)\n        dist[to] = dist[v] + 1\n\nif all(d<N for d in dist) and sum(dist) == ss[0]:\n    for a,b in es:\n        print(a+1, b+1)\nelse:\n    print(-1)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: