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>
using namespace std;
#define Maxn 100005
int n,id[Maxn],par[Maxn],sz[Maxn];
long long a[Maxn];
map <long long,int> mp;
int main()	
{
	scanf("%d",&n);
	for (int i=1;i<=n;++i)
	{
		scanf("%lld",&a[i]);
		mp[a[i]]=i;
		id[i]=i;
		sz[i]=1;
	}
	sort(id+1,id+n+1,[&](const int &x,const int &y)->bool{return a[x]>a[y];});
	for (int i=1;i<n;++i)
	{
		int x=id[i];
		par[x]=mp[a[x]-n+2*sz[x]];
		if (!par[x]) return (int)puts("-1")*0;
		sz[par[x]]+=sz[x];
	}
	for (int i=1;i<n;++i) a[id[n]]-=sz[id[i]];
	if (a[id[n]]) return (int)puts("-1")*0;
	for (int i=1;i<n;++i) printf("%d %d\n",id[i],par[id[i]]);
	return 0;
}