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())
src = [int(input()) for i in range(N)]
idx = {a:i for i,a in enumerate(src)}

size = [1] * N
ss = list(sorted(src))

es = []
gr = [[] for i in range(N)]
while len(ss) > 1:
    a = ss.pop()
    k = size[idx[a]]
    b = a + 2*k - N
    if b == a or b not in idx:
        print(-1)
        exit()
    size[idx[b]] += k
    ai,bi = idx[a],idx[b]
    es.append((ai,bi))
    gr[ai].append(bi)
    gr[bi].append(ai)

from collections import deque
dist = [N] * N
dist[idx[ss[0]]] = 0
q = deque([idx[ss[0]]])
while q:
    v = q.popleft()
    for to in gr[v]:
        if dist[to] < N: continue
        q.append(to)
        dist[to] = dist[v] + 1

if all(d<N for d in dist) and sum(dist) == ss[0]:
    for a,b in es:
        print(a+1, b+1)
else:
    print(-1)