Distance Sums

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

inputFormat

Input

Input is given from Standard Input in the following format:

N D_1 D_2 : D_N

outputFormat

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

样例

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

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

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