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: Accepted)

#include <iostream>
#include <algorithm>
#include <map>
#include <vector>

using namespace std;

typedef long long ll;

int N;
ll D[100005];
ll parent[100005];
map<ll,int> tree_sizes;

map<ll,int> D_to_old;
int new_to_old[100005];

int main() {
        cin >> N;
        for (int i=0; i<N; i++) {
                cin >> D[i];
                tree_sizes[D[i]] = 1;
                D_to_old[D[i]] = i;
                parent[i] = -1;
        }

        sort(D,D+N);

        for (int i=0; i<N; i++) {
                new_to_old[i] = D_to_old[D[i]];
        }

        ll tot_depth = 0;
        for (int i=N-1; i>=1; i--) {
                if (N - 2*tree_sizes[D[i]] <= 0) {
                        cout << "-1\n";
                        return 0;
                }

                auto new_parent = tree_sizes.find(D[i] - (N - 2*tree_sizes[D[i]]));
                if (new_parent == tree_sizes.end()) {
                        cout << "-1\n";
                        return 0;
                }

                parent[new_to_old[i]] = D_to_old[new_parent->first];
                new_parent->second += tree_sizes[D[i]];
                tot_depth += tree_sizes[D[i]];
        }

        if (D[0] != tot_depth) {
                cout << "-1\n";
                return 0;
        }

        for (int i=0; i<N; i++) {
                if (parent[i] != -1) {
                        cout << i+1 << " " << parent[i]+1 << endl;
                }
        }
}