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 il inline
#define int long long
const int N=1e5+5;

int n,m,D,sz[N],U[N],V[N];
struct node{int id,p;}d[N];

il bool operator < (node a,node b){return a.p<b.p;}

signed main()
{
	scanf("%lld",&n); int i,f,dis;
	for (i=1; i<=n; i++) scanf("%lld",&d[i].p),d[i].id=i,sz[i]=1;
	std::sort(d+1,d+n+1);
	
	for (i=n; i>1; i--)
	{
		f=std::lower_bound(d+1,d+n+1,(node){0,dis=d[i].p-n+sz[i]+sz[i]})-d;
		if (dis!=d[f].p) return puts("-1"),0;
		U[++m]=d[i].id,V[m]=d[f].id,sz[f]+=sz[i],D+=sz[i];
	}
	if (D!=d[1].p) return puts("-1"),0;
	for (i=1; i<n; i++) printf("%lld %lld\n",U[i],V[i]);
	
	return 0;
}