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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define IL inline
#define _ 1000005
#define ll long long
using namespace std ;

IL ll gi(){
	ll data = 0 , m = 1; char ch = 0;
	while(ch!='-' && (ch<'0'||ch>'9')) ch = getchar();
	if(ch == '-'){m = 0 ; ch = getchar() ; }
	while(ch >= '0' && ch <= '9'){data = (data<<1) + (data<<3) + (ch^48) ; ch = getchar(); }
	return (m) ? data : -data ; 
}

ll dis[_],fa[_],sz[_],m,n ; 

IL bool cmp(ll A , ll B){return A > B ; }

int main() {
	n = gi() ;
	for(int i = 1; i <= n; i ++) dis[i] = gi() ;
	sort(dis + 1 , dis + n + 1) ;
	//for(int i = 1; i <= n; i ++) cout << dis[i] << " " ; cout << endl ;
	dis[n + 1] = 1e18 ; 
	for(int i = n; i > 1; i --) {
		sz[i] ++ ; 
		ll ds = dis[i] + 2 * sz[i] - n ;
		int ps = lower_bound(dis + 1 , dis + n + 2 , ds) - dis ;
		//cout << i << "  sz="<<sz[i]<<"  ds="<<ds<<"  ps="<<ps<<endl ;
		if(ps == n + 1) return puts("-1") , 0 ;
		fa[i] = ps ;
		sz[ps] += sz[i] ; 
	}
	sz[1] ++ ; 
	for(int i = 2; i <= n; i ++) cout << fa[i] << " " << i << endl ;
	return 0 ; 
}