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 = "#!/usr/bin/env python3\nimport sys\n\nsys.setrecursionlimit(101010)\n\ndef dfs(v, adj_list, depth, visited):\n    visited[v] = True\n    x = depth\n    for w in adj_list[v]:\n        if not visited[w]:\n            x += dfs(w, adj_list, depth + 1, visited)\n\n    return x\n\n\ndef solve(n, d):\n\n    if n < 7:\n        print((-1))\n        return\n\n    d.sort()\n    w = [1] * n\n    edges = []\n    adj_list = [[] for _ in range(n)]\n    for j in range(n - 1, 0, -1):\n        di, i = d[j]\n        pdi = di - n + 2 * w[i]\n        p = None\n        lo, hi = 0, j\n        while lo < hi:\n            mid = (lo + hi) // 2\n            xdi, xi = d[mid]\n            if xdi == pdi:\n                p = xi\n                break\n            elif xdi < pdi:\n                lo = mid + 1\n            else:\n                hi = mid\n        if p is None:\n            print((-1))\n            return\n        u, v = i, p\n        if v < u:\n            u, v = v, u\n        edges.append((u + 1, v + 1))\n        adj_list[u].append(v)\n        adj_list[v].append(u)\n        w[p] += w[i]\n\n    d0, r = d[0]\n    visited = [False] * n\n    x = dfs(r, adj_list, 0, visited)\n    if x != d0:\n        print((-1))\n        return\n\n    edges.sort()\n    for uv in edges:\n        u, v = uv\n        print(('{} {}'.format(u, v)))\n\n\n\ndef main():\n    n = input()\n    n = int(n)\n    d = []\n    for i in range(n):\n        di = input()\n        di = int(di)\n        d.append((di, i))\n\n\n    solve(n, d)\n\n\ndef __starting_point():\n    main()\n\n\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14025