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 int long long
using namespace std;

inline int read()
{
	int x=0,f=1; char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1; ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0'; ch=getchar();}
	return x*f;
}
map<int,int> M1,M2,W1;
int s1[200010],pa[200010];
signed main()
{
	int n=read();
	for(int i=1;i<=n;i++)
	{
		int x=read();
		M1[x]=i; M2[x]=1;
		s1[i]=x; W1[x]=0;
	}
	sort(s1+1,s1+1+n);
	for(int i=n;i>1;i--)
	{
		int id=M1[s1[i]],sz=M2[s1[i]],td=s1[i]+2*sz-n;	
		if(td==s1[i]) continue;	
		pa[id]=M1[td]; M2[td]+=sz; W1[td]+=W1[s1[i]]+sz;
	}
	if(M2[s1[1]]!=n||W1[s1[1]]!=s1[1]) puts("-1"),exit(0);
	for(int i=1;i<=n;i++) if(pa[i])
		printf("%lld %lld\n",i,pa[i]);
	return 0;
}