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)

#pragma GCC optimiz(O2)

#include <bits/stdc++.h>

#define rg register
using namespace std;
typedef long long ll;

template<typename T>
inline bool read(T &n) {
    T ans = 0, flag = 1;
    char ch;
    while ((ch = getchar()) < '0' || ch > '9') if (ch == '-') flag = -1; else if (ch == EOF) return false;
    ans = ch - '0';
    while ((ch = getchar()) >= '0' && ch <= '9') ans = ans * 10 + ch - '0';
    n = ans * flag;
    return true;
}

inline ll read() {
    ll ans = 0, flag = 1;
    char ch;
    while ((ch = getchar()) < '0' || ch > '9') if (ch == '-') flag = -1;
    ans = ch - '0';
    while ((ch = getchar()) >= '0' && ch <= '9') ans = ans * 10 + ch - '0';
    return ans * flag;
};
const int maxn = 100005;
struct NODE {
    ll val, ord;
    bool operator<(NODE b) const {
        return val < b.val;
    }
} node[maxn];
int siz[maxn],fa[maxn];
unordered_map<ll,int> unM;
int main() {
    int n;
    read(n);priority_queue<NODE> pq;
    for (rg int i = 1; i <= n; ++i) {
        siz[i] = 1;
        read(node[i].val);
        node[i].ord = i;
        pq.push(node[i]);
        unM[node[i].val]=i;
    }
    for(rg int i=n;i>=2;i--){
        NODE now=pq.top();pq.pop();
        if(unM.find(now.val+2*siz[now.ord]-n)==unM.end()){
            puts("-1");return 0;
        }
        fa[now.ord]=unM[now.val+2*siz[now.ord]-n];
        siz[fa[now.ord]]+=siz[now.ord];
    }
    for(rg int i=1;i<=n;i++){
        if(fa[i]) cout<<i<<' '<<fa[i]<<endl;
    }
    return 0;
}