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 rep(i,x,y) for (int i=(x);i<=(y);i++)
#define ll long long
using namespace std;
const int N=1e5+5;
int n,id[N],fa[N],siz[N]; ll a[N]; map<ll,int> mp;
bool cmp(int x,int y){ return a[x]>a[y]; }
int main(){
	scanf("%d",&n);
	rep (i,1,n){
		scanf("%lld",&a[i]);
		mp[a[i]]=i; id[i]=i; siz[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*siz[x]];
		if (!fa[x]) return puts("-1"),0;
		siz[fa[x]]+=siz[x];
	}
	rep (i,1,n-1) a[id[n]]-=siz[id[i]];
	if (a[id[n]]) return puts("-1"),0;
	rep (i,1,n-1) printf("%d %d\n",id[i],fa[id[i]]);
	return 0;
}