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<cstdio>
#include<algorithm>
typedef long long ll;
const int MaxN=100010;
int N,V[MaxN],fa[MaxN],siz[MaxN];
ll D[MaxN];
bool cmp(int i,int j){return D[i]<D[j];}
int main(){
	scanf("%d",&N);
	for(int i=1;i<=N;i++)scanf("%lld",D+i),V[i-1]=i;
	std::sort(V,V+N,cmp);
	ll D0=0;
	for(int*i=V+N;--i>V;){
		D0+=siz[*i]++;
		D[*i]-=N-2*siz[*i];
		int*j=std::lower_bound(V,i,*i,cmp);
		if(j<i&&D[*j]==D[*i])siz[fa[*i]=*j]+=siz[*i];
		else return puts("-1"),0;
	}
	if(D0+N-1!=D[*V])return puts("-1"),0;
	for(int*i=V+N;--i>V;)printf("%d %d\n",*i,fa[*i]); 
}