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;
#define MN 100000
pair<long long,int> p[MN+5];
int s[MN+5];long long S[MN+5];
vector< pair<int,int> > ans;
int main()
{
	int n,i;
	scanf("%d",&n);
	for(i=1;i<=n;++i)scanf("%lld",&p[i].first),p[i].second=i,s[i]=1;
	sort(p+1,p+n+1);
	for(i=n;i>1;--i)
	{
		if(n-2*s[i]<0)return 0*puts("-1");
		int x=lower_bound(p+1,p+n+1,make_pair(p[i].first-n+2*s[i],0))-p;
		if(p[x].first!=p[i].first-n+2*s[i])return 0*puts("-1");
		s[x]+=s[i];S[x]+=S[i]+s[i];ans.push_back(make_pair(p[x].second,p[i].second));
	}
	if(S[1]!=p[1].first)return 0*puts("-1");
	for(i=0;i<ans.size();++i)printf("%d %d\n",ans[i].first,ans[i].second);
}