Problem:
Score : 900 points

Problem Statement

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 1

7
10
15
13
18
11
14
19

Sample Output 1

1 2
1 3
1 5
3 4
5 6
6 7

The tree shown below satisfies the conditions.

Sample Input 2

2
1
2

Sample Output 2

-1

Sample Input 3

15
57
62
47
45
42
74
90
75
54
50
66
63
77
87
51

Sample Output 3

1 10
1 11
2 8
2 15
3 5
3 9
4 5
4 10
5 15
6 12
6 14
7 13
9 12
11 13

Solution in PyPy3 (2.4.0) (judge verdict: Runtime Error)

from collections import Counter
import sys
def muri():
    print(-1)
    sys.exit()
N = int(input())
#D = [int(sys.stdin.readline()) for _ in range(N)]
D = list(map(int, input().split()))
Didx = list(range(1, N+1))
Didx.sort(key = lambda x: -D[x-1])
H = {d: i for i, d in enumerate(D, 1)}
H = Counter(H)
D = [0] + D
K = [0]*(N+1)
Ans = []
for vn in Didx[:-1]:
    if K[vn] == 0:
        K[vn] = 1
    p = H[D[vn] - (N - 2*K[vn])]
    if not p:
        muri()
    Ans.append((vn, p))
    K[p] += K[vn] + 1
s = set()

Edge = [[] for _ in range(N+1)]
for a in Ans:
    x, y = a
    Edge[x].append(y)
    Edge[y].append(x)

dist = [10**9+7]*(N+1)
dist[0] = 0
dist[1] = 0
stack = [1]
visited = set([1])
while stack:
    vn = stack.pop()
    for vf in Edge[vn]:
        if vf not in visited:
            visited.add(vf)
            dist[vf] = 1 + dist[vn]
            stack.append(vf)
if D[1] != sum(dist[1:]):
    muri()

for a in Ans:
    print(*a)