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<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<map>
#include<vector>
using namespace std;
const int N=100005;
long long d[N],m[N],dist[N];int id[N];
map<long long,int> ma;
bool cmp1(int i,int j){return d[i]>d[j];}
vector<int> ansu,ansv;
int n;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%lld",d+i);
		id[i]=i;m[i]=1;
		ma[d[i]]=i;
	}
	sort(id+1,id+1+n,cmp1);
	for(int i=1;i<n;i++){
		long long dv=d[id[i]]+2*m[id[i]]-n;
		if(ma[dv]==0){puts("-1");return 0;}
		int v=ma[dv];
		ansu.push_back(id[i]);
		ansv.push_back(v);
		m[v]+=m[id[i]];
		dist[v]+=dist[id[i]]+m[id[i]];
	}
	if(dist[id[n]]!=d[id[n]]) puts("-1");
	else
		for(int i=0;i<ansu.size();i++) printf("%d %d\n",ansu[i],ansv[i]);
}