Problem: 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

Solution (in PYTHON3):

Solution:
import sys
input = sys.stdin.readline

N = int(input())
D = [None] + [int(input()) for _ in range(N)]

parent = [None] * (N+1)
size = [None] + [1] * N # 部分木の頂点数、自分を含む
d_to_i = {d:i for i,d in enumerate(D)}
D_desc = sorted(D[1:],reverse=True)
D_subtree = [0] * (N+1)
edges = []

bl = True
for d in D_desc[:-1]:
    i = d_to_i[d]
    d_parent = d - N + 2*size[i]
    if d_parent not in d_to_i:
        bl = False
        break
    p = d_to_i[d_parent]
    edges.append('{} {}'.format(i,p))
    parent[i] = p
    size[p] += size[i]
    D_subtree[p] += D_subtree[i] + size[i]

root = d_to_i[D_desc[-1]]
bl &= (D_subtree[root] == D[root])

if bl:
    print('\n'.join(edges))
else:
    print(-1)