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>
#include<map>
using namespace std;
const int N=1e5+5;
int n,p[N],fa[N],sz[N],dep[N];long long d[N];
map<long long,int>Map;
bool cmp(int x,int y){
	return d[x]>d[y];
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i){
		scanf("%lld",&d[i]);
		Map[d[i]]=i;p[i]=i;sz[i]=1;
	}
	sort(p+1,p+n+1,cmp);
	for(int i=1;i<n;++i){
		int x=p[i];
		fa[x]=Map[d[x]-n+sz[x]+sz[x]];
		if(!fa[x]||fa[x]==x)return puts("-1"),0;
		sz[fa[x]]+=sz[x];
	}
	long long sum=0;
	for(int i=n-1;i;--i)dep[p[i]]=dep[fa[p[i]]]+1,sum+=dep[p[i]];
	if(sum!=d[p[n]])return puts("-1"),0;
	for(int i=1;i<n;++i)printf("%d %d\n",p[i],fa[p[i]]);
	return 0;
}