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<algorithm> 
#include<cstdio>
#define N 100001
using namespace std;
int b[N],f[N],h[N],i,n,s[N];long long a[N],t;
inline bool cmp(int u,int v){return a[u]<a[v];}
int main()
{
	scanf("%d",&n);
	for(i=1;i<=n;i++)scanf("%lld",a+i),s[b[i]=i]=1;
	sort(b+1,b+n+1,cmp);
	for(i=n;i>1;i--)
	{
		if(s[b[i]]<<1>=n)return 0*puts("-1");
		*a=a[b[i]]-n+(s[b[i]]<<1),f[b[i]]=lower_bound(b+1,b+n+1,0,cmp)-b;
		if(f[b[i]]>n||a[b[f[b[i]]]]!=*a)return 0*puts("-1");
		s[f[b[i]]=b[f[b[i]]]]+=s[b[i]];
	}
	for(i=2;i<=n;i++)t+=h[b[i]]=h[f[b[i]]]+1;
	if(t!=a[b[1]])return 0*puts("-1");
	for(i=2;i<=n;i++)printf("%d %d\n",b[i],f[b[i]]);
	return 0;
}