Problem: 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.

Examples

Input

7
10
15
13
18
11
14
19


Output

1 2
1 3
1 5
3 4
5 6
6 7


Input

2
1
2


Output

-1


Input

15
57
62
47
45
42
74
90
75
54
50
66
63
77
87
51


Output

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 CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

typedef long long LL;
#define repp(i,a,b) for(int i = (int)(a) ; i < (int)(b) ; ++i)
#define repm(i,a,b) for(int i = (int)(a) ; i > (int)(b) ; --i)

int main(){
	int N; cin >> N;
	vector<LL> D(N),dp(N,0);
	vector<int> s(N),sz(N,1),p(N,-1);
	map<LL,int> M;
	repp(i,0,N){
		cin >> D[i];
		M[D[i]] = i;
		s[i] = i;
	}
	sort(s.begin(),s.end(),[&](const int &i, const int &j){return D[i] > D[j];});
	repp(i,0,N-1){
		auto it = M.find(D[s[i]]-N+2+(sz[s[i]]-1)*2);
		if(it == M.end() || (*it).first >= D[s[i]]) return cout << -1 << endl, 0;
		p[s[i]] = (*it).second;
		dp[(*it).second] += sz[s[i]]+dp[s[i]];
		sz[(*it).second] += sz[s[i]];
	}
	if(D[s[N-1]] != dp[s[N-1]]) return cout << -1 << endl, 0;
	repp(i,0,N-1) cout << s[i]+1 << ' ' << p[s[i]]+1 << endl;
	return 0;
}