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)

//              +-- -- --++-- +-In the name of ALLAH-+ --++-- -- --+              \\

#include <bits/stdc++.h>

#define int ll

#define F first
#define S second
#define _sz(x) (int)x.size()

using namespace std ;
using ll = long long ;
using ld = long double ;
using pii = pair <int , int> ;

int const N = 1e5 + 20 ;
int n , d[N] , sz[N] ;
map <int , int> mp ;
vector <pii> edges ;

void err () {
	cout << -1 << '\n' ;
	exit(0) ;
}

int32_t main(){
	ios::sync_with_stdio(false) , cin.tie(0) , cout.tie(0) ;

	cin >> n ;

	for (int i = 0 ; i < n ; i ++) cin >> d[i] , mp[d[i]] = i , sz[i] = 1 ;

	sort(d , d + n , greater<int>()) ;

	for (int i = 0 ; i < n - 1 ; i ++) {
		int v = mp[d[i]] ;
		int k = d[i] - n + 2 * sz[v] ;

		if (k == d[i] || !mp.count(k)) err() ;

		int p = mp[k] ;

		sz[p] += sz[v] ;
		edges.push_back({p , v}) ;
	}

	for (pii p : edges) cout << p.F + 1 << ' ' << p.S + 1 << '\n' ;
}