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:
def solve(n, ddd):
    dsd = {d: i for i, d in enumerate(ddd)}
    child_cnt = [1] * n
    child_dist = [0] * n
    buf = []
    srt = sorted(dsd.items(), reverse=True)
    for d, i in srt[:-1]:
        cc = child_cnt[i]
        pd = d - (n - cc * 2)
        if pd == d or pd not in dsd:
            return -1
        pi = dsd[pd]
        buf.append((pi + 1, i + 1))
        child_cnt[pi] += cc
        child_dist[pi] += child_dist[i] + cc

    md, mi = srt[-1]
    if md != child_dist[mi]:
        return -1
    return buf


n = int(input())
ddd = list(map(int, (input() for _ in range(n))))
res = solve(n, ddd)
if res == -1:
    print(-1)
else:
    print('\n'.join('{} {}'.format(*l) for l in res))