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 <time.h>

#include <stdlib.h>
#include <cstdint>
#include <cassert>
#include <algorithm>
#include <functional>
#include <iostream>
#include <limits>
#include <cstdint>
#include <cassert>
#include <algorithm>
#include <functional>
#include <iostream>
#include <limits>
#include <vector>
#include <map>
using namespace std;
struct condition{
	int64_t vertex;
	int64_t total;
};
struct current{
	int64_t parent;
	int64_t vertex_num;
};
struct edge{
	int64_t v1;
	int64_t v2;
};
bool operator< (const condition& a,const condition& b){
	return a.total>b.total;
}
int main() {

	int64_t n;
	cin>>n;
	std::vector<condition> cd;
	vector<edge> ans;
	ans.reserve(n);
	cd.reserve(n);
	for(int i=0;i<n;i++){
		int64_t temp;
		cin>>temp;
		cd.push_back(condition{i+1,temp});
	}
	bool ans_possible=true;
	sort(cd.begin(),cd.end());
	map<int64_t,vector<current> > flow;
	for(auto i=cd.begin();i!=cd.end();i++){
		bool islast = (i==cd.end()-1);
		int64_t sum_vertex=0;

		if(flow.count(i->total)){
			vector<current>& t=flow.at(i->total);
			int64_t total_cost=0;
			for(auto k=t.begin();k!=t.end();k++){
				ans.push_back(edge{k->parent,i->vertex});
				sum_vertex+=(k->vertex_num);
				total_cost+=((k->vertex_num)*(k->vertex_num+1))/2;
			}
			ans_possible=(total_cost==i->total);

			flow.erase(i->total);
		}else{
			ans_possible=false;
		}

		sum_vertex++;

		int64_t parent_value=i->total-(n-2*sum_vertex);
		if(!islast&&parent_value>=i->total){
			ans_possible=false;
			break;
		}
		if(flow.count(parent_value)){
			flow.at(parent_value).push_back(current{i->vertex,sum_vertex});
		}else{
			vector<current> temp2;
			temp2.push_back(current{i->vertex,sum_vertex});
			flow.emplace(parent_value,temp2);
		}

	}
	if(flow.size()==1&&ans_possible&&ans.size()==(n-1)){
		for(auto i=ans.begin();i!=ans.end();i++){
			cout<<i->v1<<" "<<i->v2<<endl;
		}
	}else{
		cout<<-1<<endl;
	}





	return 0;

}