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>
using namespace std;
#define int long  long
#define N 100010
struct node{
	int x,id;
	bool operator<(const node &a) const{
		return x>a.x;
	}
}D[N];
int sz[N],fa[N];
map<int,int>mp;
signed main(){
	int n;
	scanf("%lld",&n);
	for (int i=1;i<=n;i++){
		scanf("%lld",&D[i].x);
		D[i].id=i;
		mp[D[i].x]=i;
	}
	sort(D+1,D+1+n);
	for (int i=1;i<=n;i++) sz[i]=1;
	for (int i=1;i<n;i++){
		int x=D[i].id;
		fa[x]=mp[D[i].x-n+2*sz[x]];
		if (!fa[x])  return puts("-1"),0;
		sz[fa[x]]+=sz[x];
	}
	for (int i=1;i<n;i++) D[n].x-=sz[D[i].id];
	if (D[n].x) return puts("-1"),0;
	for (int i=1;i<n;i++) printf("%lld %lld\n",fa[D[i].id],D[i].id);
	return 0;
}