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 <iostream>
#include <vector>
#include <map>
#include <algorithm>
#include <utility>
#define llint long long

using namespace std;
typedef pair<llint, llint> P;

llint N;
llint d[100005];
P D[100005];
vector<llint> G[100005];
map<llint, vector<P> > mp;

int main(void)
{
	cin >> N;
	for(int i = 1; i <= N; i++) cin >> d[i];
	for(llint i = 1; i <= N; i++) D[i] = make_pair(d[i], i);
	sort(D+1, D+N+1);
	reverse(D+1, D+N+1);
	
	for(int i = 1; i <= N; i++){
		if(mp.count(D[i].first) == 0){
			llint p = D[i].first+N-2;
			if(p > D[i].first) continue;
			mp[p].push_back(make_pair(D[i].second, 1));
		}
		else{
			llint x = 0;
			for(int j = 0; j < mp[D[i].first].size(); j++){
				G[D[i].second].push_back(mp[D[i].first][j].first);
				G[mp[D[i].first][j].first].push_back(D[i].second);
				x += mp[D[i].first][j].second;
			}
			x++;
			llint p = D[i].first+N-2*x;
			if(p > D[i].first) continue;
			mp[p].push_back(make_pair(D[i].second, x));
		}
	}
	vector<P> ans;
	for(int i = 1; i <= N; i++){
		for(int j = 0; j < G[i].size(); j++){
			if(G[i][j] > i) ans.push_back(make_pair(i, G[i][j]));
		}
	}
	if(ans.size() < N-1) cout << "-1" << endl;
	else{
		for(int i = 0; i < ans.size(); i++) cout << ans[i].first << " " << ans[i].second << endl;
	}
	
	return 0;
}