201033: [AtCoder]ARC103 F - Distance Sums

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