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 <cstdio>
#include <map>

int n;
struct point{
	long long D;
	int id;
}num[100001];
std::map<long long,int>map;
int size[100001],fa[100001],dep[100001];
bool cmp(const point &a,const point &b){return a.D>b.D;}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%lld",&num[i].D),num[i].id=map[num[i].D]=i,size[i]=1;
	std::sort(num+1,num+n+1,cmp);
	for(int i=1;i<n;i++)
		if(!(fa[i]=map[num[i].D+(size[num[i].id])-(n-size[num[i].id])])||(fa[i]==num[i].id))
			{puts("-1");return 0;}
		else size[fa[i]]+=size[num[i].id];
	for(int i=n-1;i;i--)num[n].D-=(dep[num[i].id]=dep[fa[i]]+1);
	if(num[n].D){puts("-1");return 0;}
	for(int i=1;i<n;i++)printf("%d %d\n",fa[i],num[i].id);
}