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 <bits/stdc++.h>
#define show(x) std::cerr << #x << " = " << x << std::endl
using ll = long long;
int main()
{
    int N;
    std::cin >> N;
    std::map<ll, int> mp, mp2;
    std::vector<ll> D(N);
    for (int i = 0; i < N; i++) { std::cin >> D[i], mp[D[i]] = i; }
    std::sort(D.begin(), D.end(), std::greater<ll>{});
    for (int i = 0; i < N; i++) { mp2[D[i]] = i; }
    std::vector<std::vector<int>> edge(N);
    std::vector<int> sub(N, 1);
    for (int i = 0; i < N - 1; i++) {
        const ll obj = D[i] - (N - 2 * sub[i]);
        if (obj == D[i] or mp2.find(obj) == mp2.end()) { return std::cout << -1 << std::endl, 0; }
        const int prev = mp2[obj];
        edge[mp[obj]].push_back(mp[D[i]]), sub[prev] += sub[i];
    }
    ll sum = 0;
    auto check = [&](auto&& self, const int s, const int d) -> void {
        sum += d;
        for (const int to : edge[s]) { self(self, to, d + 1); }
    };
    check(check, mp[D[N - 1]], 0);
    if (D[N - 1] == sum) {
        for (int i = 0; i < N; i++) {
            for (const int to : edge[i]) {
                std::cout << i + 1 << " " << to + 1 << std::endl;
            }
        }
    } else {
        std::cout << -1 << std::endl;
    }
    return 0;
}