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<algorithm>
#include<iostream>
#include<cstdio>
#define LL long long
using namespace std;
int n;
LL dis,D;
const int N=100010;
int siz[N],X[N],Y[N];
struct dian
{
	LL dis;int id;
	friend bool operator <(const dian &a,const dian &b)
		{return a.dis<b.dis;}
}d[N];
int main()
{
	cin>>n;
	for(int i=1;i<=n;++i)
		scanf("%lld",&D),d[i]=(dian){D,i},siz[i]=1;
	sort(d+1,d+1+n);
	for(int i=n,pos;i>1;--i)
	{
		D=d[i].dis-n+(siz[i]<<1);
		pos=lower_bound(d+1,d+1+n,(dian){D,0})-d;
		if(d[pos].dis!=D)return puts("-1")==2333;
		X[i]=d[i].id;Y[i]=d[pos].id;
		siz[pos]+=siz[i];dis+=siz[i];
	}
	if(dis!=d[1].dis)return puts("-1")==2333;
	for(int i=2;i<=n;++i)printf("%d %d\n",X[i],Y[i]);
	return 0;
}