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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;

public class Main {
	static final Reader in = new Reader();
	static final PrintWriter out = new PrintWriter(System.out);
	
	public static void main(String[] args) {
		int n=in.nextInt();
		Pair[] d = new Pair[n];
		int[] s = new int[n], p = new int[n];
		Map<Long, Integer> mp = new HashMap<Long, Integer>();
		for(int i=0; i<n; ++i) {
			d[i] = new Pair(in.nextLong(), i);
			mp.put(d[i].a, i);
			s[i]=1;
		}
		Arrays.sort(d);
		for(int i=0; i<n-1; ++i) {
			int u=d[i].b;
			p[u]=mp.getOrDefault(d[i].a-n+2*s[u], -1);
			if(d[i].a-n+2*s[u]>=d[i].a||p[u]==-1) {
				System.out.println(-1);
				return;
			}
			s[p[u]]+=s[u];
		}
		for(int i=1; i<n; ++i)
			out.println((i+1)+" "+(p[i]+1));
		out.close();
	}
	
	static class Pair implements Comparable<Pair> {
		long a;
		int b;
		Pair(long a, int b) {
			this.a=a;
			this.b=b;
		}
		public int compareTo(Pair o) {
			return -Long.compare(a, o.a);
		}
	}
	
	static class Reader {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;
		
		String next() {
			while(st==null||!st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch(Exception e) {}
			}
			return st.nextToken();
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
}