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())
numlist=list(map(int,(input() for _ in range(N))))
numdict={y:x for x,y in enumerate(numlist)}
sorted_list=sorted(numdict.items(),reverse=True)

nextS=lambda Snow,child : Snow+2*child-N

amount_of_child=[1]*N
sum_of_distance_of_child=[0]*N
branch_list=[]

for S,num in sorted_list:
  nS=nextS(S,amount_of_child[num])
  if nS in numdict:
    nextnum=numdict[nS]
    branch_list.append([num+1,nextnum+1])
    amount_of_child[nextnum]+=amount_of_child[num]
    sum_of_distance_of_child[nextnum]+=(sum_of_distance_of_child[num]+amount_of_child[num])
    if amount_of_child[nextnum]==N:
      break
  else:
    print (-1)
    exit()

if sorted_list[-1][0]==sum_of_distance_of_child[sorted_list[-1][1]]:
  for _ in range(N-1):
    x,y=branch_list.pop()
    print(x,y)
else:
  print (-1)
exit()