题目描述
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.
Examples
Input
7
10
15
13
18
11
14
19
Output
1 2
1 3
1 5
3 4
5 6
6 7
Input
2
1
2
Output
-1
Input
15
57
62
47
45
42
74
90
75
54
50
66
63
77
87
51
Output
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
输入格式
见题面
输出格式
见题面