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>
using namespace std;
int n,size[100010],fa[100010],tmp=0,cnt=0;
long long d[100010];
map<long long,int>ma;
struct node{
	long long w;
	int id;
	bool operator <(const node &b)const{
		return w<b.w;
	}
};
priority_queue<node>q;
int main(){
	ma.clear();
	while(q.size()) q.pop();
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%lld",&d[i]);
		ma[d[i]]=i,size[i]=1;
		q.push((node){d[i],i});
	}
	while(q.size()){
		node now=q.top();q.pop();
		if(size[now.id]==1) tmp++;
		fa[now.id]=ma[d[now.id]+size[now.id]*2-n];
		size[fa[now.id]]+=size[now.id];
	}
	for(int i=1;i<=n;i++) if(size[i]==1) cnt++;
	if(cnt==tmp){
		for(int i=1;i<=n;i++){
			if(fa[i]) printf("%d %d\n",i,fa[i]);
		}
	}
	else printf("-1\n"); 
}