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<cstring>
#include<algorithm>
using namespace std;
typedef long long ll;
struct pt
{
	ll val;
	int id;
	pt(ll val=0,int id=0):val(val),id(id){}
	bool operator<(const pt x) const
	{
		return val>x.val;
	}
}a[100005];
int n,e[100005][2],sz[100005];
ll f[100005];
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		scanf("%lld",&a[i].val),a[i].id=i;
	for(int i=1;i<=n;i++)
		sz[i]=1;
	sort(a+1,a+n+1);
	for(int i=1;i<n;i++)
	{
		int u=a[i].id,v;
		int nw=lower_bound(a+1,a+n+1,pt(a[i].val-n+2*sz[u]))-a;
		if(a[nw].val!=a[i].val-n+2*sz[u])
		{
			printf("-1");
			return 0;
		}
		v=a[nw].id;
		e[i][0]=u,e[i][1]=v;
		sz[v]+=sz[u],f[v]+=f[u]+sz[u];
	}
	if(f[a[n].id]!=a[n].val)
	{
		printf("-1");
		return 0;
	}
	for(int i=1;i<n;i++)
		printf("%d %d\n",e[i][0],e[i][1]);
	return 0;
}