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>
using namespace std;
const int N=1e5+5;
int n;
long long d[N],cur[N];
int id[N],sz[N],par[N];
bool cmp(int a,int b){return d[a]>d[b];}
int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
	{
		scanf("%lld",&d[i]);
		id[i]=i;
		sz[i]=1;
	}
	sort(id+1,id+n+1,cmp);
	for (int i=1;i<n;i++)
	{
		long long dpar=d[id[i]]+sz[id[i]]-(n-sz[id[i]]);
		for (int j=i+1;j<=n;j++)
			if (dpar==d[id[j]])
			{
				par[id[i]]=id[j];
				cur[id[j]]+=cur[id[i]]+sz[id[i]];
				sz[id[j]]+=sz[id[i]];
			}
			else
				if (dpar>d[id[j]])
					break;
		if (!par[id[i]])
			break;
	}
	if (cur[id[n]]!=d[id[n]])
		printf("-1\n");
	else
		for (int i=1;i<n;i++)
			printf("%d %d\n",id[i],par[id[i]]);
	return 0;
}