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<algorithm>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<map>
#define rep(i,x,y) for(int i=(x);i<=(y);i++)
using namespace std;
typedef long long ll;
int n;
const int N=200005;
map<long long,int> mp;
long long a[N];
int id[N];
int fa[N],size[N];
bool cmp(int x,int y){return a[x]>a[y];}
int main()
{
//freopen("input.txt","r",stdin);
ios::sync_with_stdio(false);
cin.tie(0);
int n;
cin >>n;
rep(i,1,n)cin >>a[i],id[i]=i,mp[a[i]]=i,size[i]=1;
sort(id+1,id+1+n,cmp);
rep(i,1,n-1)
	{
	int x=id[i];
	fa[x]=mp[a[x]-n+2*size[x]];
	if(!fa[x])return cout <<-1,0;
	size[fa[x]]+=size[x];
	}
rep(i,1,n-1)
	{
	a[id[n]]-=size[id[i]];
	}
if (a[id[n]]) return puts("-1"),0;
rep (i,1,n-1) cout <<id[i]<<' '<<fa[id[i]]<<'\n';
return 0;
}