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 = int(raw_input())
    # D = [int(raw_input()) for i in range(N)]
    N = int(input())
    D = [int(input()) for i in range(N)]
    if sum(D) % 2 > 0:
        print ('-1')
        return
    Di = sorted([(di, i) for i, di in enumerate(D)], key = lambda x : x[0], reverse = True)
    d_to_i = {dd:i for dd, i in Di}
    # child = [[] for i in range(N)]
    ans = []
    n_child = [1] * N
    d_child = [0] * N
    for valD, node in Di:
        valD_par = valD - N + 2 * n_child[node]
        if valD_par in d_to_i.keys():
            node_par = d_to_i[valD_par]
            # child[node].append(node_par) ##
            # child[node_par].append(node)
            ans.append((node_par + 1, node + 1))
            n_child[node_par] += n_child[node]
            d_child[node_par] += n_child[node] + d_child[node]
            if n_child[node_par] == N:
                break
        else:
            print ('-1')
            return
    # check if Di satisfied or not
    d_min, i_min = Di[-1]
    if d_child[i_min] != d_min:
        print ('-1')
        return
    # for i in range(N):
    #     for j in child[i]:
    #         print str(i + 1) + ' ' + str(j + 1)
    for i,j in ans:
        print (str(i) + ' ' + str(j))

if __name__ == '__main__':
    solve()