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<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=100003;
int n;
struct Node{
	int id;
	ll d;
	bool operator < (const Node &a) const
	{
		return d>a.d;
	}
}a[N];
int siz[N],u[N],v[N];
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		a[i].id=i;
		scanf("%lld",&a[i].d);
	}
	sort(a+1,a+n+1);
	for(int i=1;i<=n;i++)
		siz[i]=1;
	ll dis=0;
	for(int i=1;i<n;i++)
	{
		ll d=a[i].d-n+siz[a[i].id]+siz[a[i].id];
		int x=lower_bound(a+1,a+n+1,(Node){0,d})-a;
		if(a[x].d!=d)
		{
			puts("-1");
			return 0;
		}
		u[i]=a[i].id,v[i]=a[x].id;
		siz[a[x].id]+=siz[a[i].id];
		dis+=siz[a[i].id];
	}
	if(dis!=a[n].d)
	{
		puts("-1");
		return 0;
	}
	for(int i=1;i<n;i++)
		printf("%d %d\n",u[i],v[i]);
	return 0;
}