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 ll long long
using namespace std;
template<typename tn> void read(tn &a){
	tn x=0,f=1; char c=' ';
	for(;!isdigit(c);c=getchar()) if(c=='-') f=-1;
	for(;isdigit(c);c=getchar()) x=x*10+c-'0';
	a=x*f;
}
int n,p[101000],s[101000],vis[101000];
ll a[101000];
vector<pair<int,int> > ans;
map<ll,int> mp;
int main(){
	read(n);
	for(int i=1;i<=n;i++){
		read(a[i]);mp[a[i]]=i;
		p[i]=i;s[i]=1;
	}
	sort(p+1,p+n+1,[&](int x,int y){
		return a[x]>a[y];
	});
	ll res=0;
	for(int i=1;i<n;i++){
		int x=p[i];
		mp.erase(a[x]);
		ll pos=a[x]+s[x]-(n-s[x]);
		if(!mp.count(pos)){puts("-1");return 0;}
		ans.emplace_back(x,mp[pos]);
		s[mp[pos]]+=s[x];res+=s[x];
	}
	if(a[p[n]]!=res){puts("-1");return 0;}
	for(auto pr:ans){
		cout<<pr.first<<' '<<pr.second<<'\n';
	}
	return 0;
}