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:
from collections import defaultdict
N = int(input())
C = defaultdict(int)
for i in range(N):
  D = int(input())
  C[D] = i + 1
E = []
H = [1] * (N + 1)
DD = sorted([[k, v] for k, v in C.items()], reverse=True)
Adj = [[] for i in range(N)]
for D, n in DD[:-1]:
  try:
    p = C[D - N + 2 * H[n]]
    if n == p:
      raise Error
    E.append([n, p])
    Adj[n - 1].append(p - 1)
    Adj[p - 1].append(n - 1)
    H[p] += H[n]
  except:
    print(-1)
    break
else:
  dist = [N] * N
  dist[DD[-1][1] - 1] = 0
  Q = [DD[-1][1] - 1] + [N] * N
  tail = 1
  for i in range(N):
    s = Q[i]
    if s == N:
      print(-1)
      break
    for adj in Adj[s]:
      if dist[adj] == N:
        dist[adj] = dist[s] + 1
        Q[tail] = adj
        tail += 1
  else:
    if sum(dist) == DD[-1][0]:
      for e in E:
        print(e[0], e[1])
    else:
      print(-1)