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<algorithm>
#include<cstring>
#include<cstdio>
using namespace std;
struct Val{
	long long d;
	int u;
}p[100010];
bool cmp(Val a,Val b)
{
	return a.d>b.d;
}
int find(int l,int r,long long t)
{
	while(l+1<r)
	{
		int mid=(l+r)>>1;
		if(p[mid].d<=t)r=mid;
		else l=mid;
	}
	if(p[r].d!=t)return -1;
	return r;
}
int u[100010],v[100010];
int siz[100010];
int main()
{
	int n;scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%lld",&p[i].d);
		p[i].u=i;
	}
	sort(p+1,p+n+1,cmp);
	long long res=0;
	for(int i=1;i<n;i++)
	{
		siz[i]++;
		u[i]=p[i].u;
		int pos=find(i,n,p[i].d+siz[i]-(n-siz[i]));
		if(pos==-1){
			printf("-1\n");
			return 0;
		}
		v[i]=p[pos].u;
		siz[pos]+=siz[i];
		res+=siz[i];
	}
	if(res!=p[n].d){
		printf("-1\n");
		return 0;
	}
	for(int i=1;i<n;i++)
		printf("%d %d\n",u[i],v[i]);
	return 0;
}