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<map>
#include<algorithm>
#define N 1000400
using namespace std;
int n,v2[N],fa[N];
long long v[N],sz[N],ds[N];
map<long long,int> tp;
bool cmp(int a,int b){return v[a]<v[b];}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%lld",&v[i]),tp[v[i]]=i,v2[i]=i,sz[i]=1;
	sort(v2+1,v2+n+1,cmp);
	for(int i=n;i>1;i--)
	{
		long long tp2=v[v2[i]]-n+sz[v2[i]]*2;
		if(!tp[tp2]){printf("-1\n");return 0;}
		int sb=tp[tp2];
		ds[sb]+=ds[v2[i]]+sz[v2[i]];
		sz[sb]+=sz[v2[i]];
		fa[v2[i]]=sb;
	}
	if(ds[v2[1]]!=v[v2[1]]){printf("-1\n");return 0;}
	for(int i=1;i<=n;i++)if(fa[i])printf("%d %d\n",i,fa[i]);
}//111222333