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 <bits/stdc++.h>
const int N=1e5+5;
using namespace std;
struct Edge{int x,y;}e[N];
struct Node{
	long long d;int id;
	bool operator <(const Node &b)const{return d<b.d;}
}d[N];
int n,cnt;
long long size[N];
long long dis;
inline Node Make(long long _d,int _id){Node t;t.d=_d,t.id=_id;return t;}
int main(){
	
	register int i;
    long long x;
	scanf("%d",&n);
	for(i=1;i<=n;++i)
		scanf("%lld",&x),d[i].d=x,d[i].id=i,size[i]=1;
	sort(d+1,d+n+1);
	for(i=n;i>=2;--i){
		long long t=d[i].d-n+size[i]*2;
		int pos=lower_bound(d+1,d+n+1,Make(t,0))-d;
		if(d[pos].d!=t) return puts("-1"),0;
		e[++cnt]=(Edge){d[i].id,d[pos].id};
		size[pos]+=size[i]; //
		dis+=size[i];
	}
	if(dis!=d[1].d) puts("-1");
	else
		for(i=1;i<=cnt;++i)
			printf("%d %d\n",e[i].x,e[i].y);
	return 0;
}