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<algorithm>
#include<cstring>
#include<cctype>
#include<cstdio>
#include<map>
#define rep(i,x,y) for(int i=x; i<=y; ++i)

using namespace std;
typedef long long LL;
const int N=100005;
int n,p[N],siz[N],fa[N];
LL d[N],d_[N];
map <LL,int> s;

bool cmp(int x,int y)
{
	return d[x]>d[y];
}

int main()
{
	scanf("%d",&n);
	rep(i,1,n) scanf("%lld",&d[i]),p[i]=i,s[d[i]]=i;
	sort(p+1,p+1+n,cmp);
	rep(i,1,n-1)
	{
		++siz[p[i]];
		LL D=d[p[i]]-n+2*siz[p[i]];
		if(D>=d[p[i]] || !s.count(D)) {puts("-1"); return 0;}
		fa[p[i]]=s[D],siz[fa[p[i]]]+=siz[p[i]];
		d_[fa[p[i]]]+=d_[p[i]]+siz[p[i]];
	}
	if(d_[p[n]]!=d[p[n]]) puts("-1");
	else rep(i,1,n-1) printf("%d %d\n",p[i],fa[p[i]]);
	return 0;
}