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 <algorithm>
#include <vector>
#include <string>
#include <map>

using namespace std;
using ll = long long;

int main() {
  int n;
  cin >> n;
  vector<ll> d(n);
  vector<int> parent(n, -1);
  vector<int> p(n);
  vector<ll> size(n, 1);
  map<ll, int> mp;
  for (int i = 0; i < n; i++) {
    cin >> d[i];
    p[i] = i;
    mp[d[i]] = i;
  }
  sort(p.begin(), p.end(), [&](int i, int j) { return d[i] > d[j]; });
  p.pop_back();
  for (int i : p) {
    ll tmp = d[i] - n + 2 * size[i];
    if (tmp < d[i] && mp.count(tmp)) {
      parent[i] = mp[tmp];
      size[parent[i]] += size[i];
    } else {
      cout << -1 << '\n';
      return 0;
    }
  }
  for (int i = 0; i < n; i++) {
    if (parent[i] != -1) {
      cout << i+1 << ' ' << parent[i]+1 << '\n';
    }
  }
}