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:
n = int(input())
d = [int(input()) for i in range(n)]

if sum(d)%2 > 0:
    print(-1)
    exit()

d = sorted([(dd, i) for i, dd in enumerate(d)], reverse = True)
d_to_i = {dd:i for dd, i in d}
n_child = [1]*n
d_child = [0]*n
ans = []
for dd, i in d:
    d_i = dd+2*n_child[i]-n
    if d_i in d_to_i.keys():
        i_next = d_to_i[d_i]
        ans.append((i+1, i_next+1))
        n_child[i_next] += n_child[i]
        d_child[i_next] += d_child[i] + n_child[i]
        if n_child[i_next] == n:
            break
    else:
        print(-1)
        exit()

d_min, i_min = d[-1]
if d_min == d_child[i_min]:
    for a in ans:
        print(*a)
else:
     print(-1)