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:
#!/usr/bin/env python3
import sys

sys.setrecursionlimit(101010)

def dfs(v, adj_list, depth, visited):
    visited[v] = True
    x = depth
    for w in adj_list[v]:
        if not visited[w]:
            x += dfs(w, adj_list, depth + 1, visited)

    return x


def solve(n, d):

    if n < 7:
        print(-1)
        return

    d.sort()
    w = [1] * n
    edges = []
    adj_list = [[] for _ in range(n)]
    for j in range(n - 1, 0, -1):
        di, i = d[j]
        pdi = di - n + 2 * w[i]
        p = None
        lo, hi = 0, j
        while lo < hi:
            mid = (lo + hi) // 2
            xdi, xi = d[mid]
            if xdi == pdi:
                p = xi
                break
            elif xdi < pdi:
                lo = mid + 1
            else:
                hi = mid
        if p is None:
            print(-1)
            return
        u, v = i, p
        if v < u:
            u, v = v, u
        edges.append((u + 1, v + 1))
        adj_list[u].append(v)
        adj_list[v].append(u)
        w[p] += w[i]

    d0, r = d[0]
    visited = [False] * n
    x = dfs(r, adj_list, 0, visited)
    if x != d0:
        print(-1)
        return

    edges.sort()
    for uv in edges:
        u, v = uv
        print('{} {}'.format(u, v))



def main():
    n = input()
    n = int(n)
    d = []
    for i in range(n):
        di = input()
        di = int(di)
        d.append((di, i))


    solve(n, d)


if __name__ == '__main__':
    main()