Problem:
Score : 900 points

Problem Statement

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.

Sample Input 1

7
10
15
13
18
11
14
19

Sample Output 1

1 2
1 3
1 5
3 4
5 6
6 7

The tree shown below satisfies the conditions.

Sample Input 2

2
1
2

Sample Output 2

-1

Sample Input 3

15
57
62
47
45
42
74
90
75
54
50
66
63
77
87
51

Sample Output 3

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 Python (3.4.3) (judge verdict: Wrong Answer)




N=int(input())
numlist=[int(input()) for _ in range(N)]
numdict={y:x+1 for x,y in enumerate(numlist)}
sorted_list=sorted(numdict.items(),reverse=True)
print (sorted_list)


nextS=lambda Snow,Bnow : Snow+2*Bnow-N
Bnow=1
branch_list=[]
Snow,num=(sorted_list[0][0],numdict.pop(sorted_list[0][0]))
while numdict:
  S=nextS(Snow,Bnow)
  if S in numdict:
    branch_list.append([num,numdict[S]])
    Bnow+=1
    Snow,num=S,numdict.pop(S)
  else:
    for x in range(1,(N-Bnow)//2):
      S=nextS(Snow,N-x)
      if S in numdict:
        x-=1
        can=[[num,S]]
        while x:
          Sbuf=S
          S=nextS(S,N-x)
          can.append([numdict[Sbuf],S])
          if not S in numdict:
            break
          x-=1
        else:
          print(can)
          for buf in can:
            branch_list.append([buf[0],numdict.pop(buf[1])])
          Bnow=len(branch_list)+1
          break
    else:
      print(branch_list)
      print(-1)
      exit()

for _ in range(N-1):
  x,y=branch_list.pop()
  print(x,y)