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 main():
    N = int(input())
    D = [int(input()) for i in range(N)]
    C = [1] * N
    T = [0] * N
    DI = {}
    for i in range(len(D)):
        DI[D[i]] = i
    D = sorted(D)
    P = [-1] * N
    while len(D) > 1:
        d = D.pop()
        i = DI[d]
        nd = d - N + C[i] * 2
        if nd in DI:
            ni = DI[nd]
        else:
            print(-1)
            return
        P[i] = ni
        C[ni] += C[i]
        T[ni] += T[i] + C[i]
    
    if D[0] == T[DI[D[0]]]:
        for i in range(N):
            if P[i] >= 0: print(i+1, P[i]+1)
    else:
        print(-1)

main()