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<bits/stdc++.h>
#define exi return puts("-1"),0
const int N=100005;
using namespace std;
typedef long long ll;
int n,no[N],sz[N],f[N],de[N];
pair<ll,int>d[N];
ll tp,ans;
map<ll,int>mp;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	scanf("%lld",&d[i].first),
	d[i].second=i,sz[i]=1;
	sort(d+1,d+n+1);
	for(int i=1;i<=n;i++)
	mp[d[i].first]=i;
	for(int i=n;i>1;i--){
		tp=d[i].first+2*sz[i]-n;
		//cerr<<d[i].first<<":"<<tp<<endl;
		if(sz[i]*2>=n||!mp[tp])exi;
		f[i]=mp[tp],sz[mp[tp]]+=sz[i];
	}
	//cerr<<"??\n";
	for(int i=2;i<=n;i++)
	de[i]=de[f[i]]+1,ans+=de[i];
	if(ans^d[1].first)exi;
	for(int i=2;i<=n;i++)
	printf("%d %d\n",d[i].second,d[f[i]].second);
}