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 fo(i,a,b)for(int i=a,_e=b;i<=_e;++i)
#define fd(i,a,b)for(int i=b,_e=a;i>=_e;--i)
#define ll long long
#define NO return printf("-1"),0
using namespace std;
const int N=1e5+5;
int n,b[N][2],bs,sz[N];
ll w[N],su;
vector<int>e[N];
unordered_map<ll,int>A;
void find(int x,int len){
	su+=len;
	for(int i:e[x])find(i,len+1);
}
int main(){
	ios::sync_with_stdio(0);
	cin>>n;
	fo(i,1,n)cin>>w[i],A[w[i]]=i,sz[i]=1;
	sort(w+1,w+n+1);
	fd(i,2,n){
		int x=A[w[i]],y;
		if(sz[x]*2>=n)NO;
		y=A[w[i]-n+sz[x]*2];
		if(!y)NO;
		++bs;b[bs][0]=x;b[bs][1]=y;
		sz[y]+=sz[x];
		e[y].push_back(x);
	}
	find(A[w[1]],0);
	if(su!=w[1])NO;
	fo(i,1,bs)printf("%d %d\n",b[i][0],b[i][1]);
}