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<cstdio>
#include<algorithm>
#define int long long
const int N=100005;
struct D{int w,x,s;}d[N];int n,he[N],to[N],nx[N];
bool cmp(D x,D y){return x.x>y.x;}
inline void wk(int w,int x,int y)
{to[w]=y,nx[w]=he[x],he[x]=w;}
int dfs(int x,int y)
{
	int z=y;
	for(int i=he[x];i;i=nx[i])
		z+=dfs(to[i],y+1);
	return z;
}
signed main()
{
	scanf("%lld",&n);
	for(int i=1;i<=n;++i)
		scanf("%lld",&d[i].x),d[i].w=i,d[i].s=1;
	std::sort(d+1,d+n+1,cmp);
	for(int i=1,x,l,r,I;i<n;++i)
	{
		for(x=0,l=i+1,r=n;l<=r;)
			I=l+r>>1,d[I].x>=d[i].x+2*d[i].s-n?(x=I,l=I+1):(r=I-1);
		if(!x||d[x].x!=d[i].x+2*d[i].s-n)
			return 0&printf("-1");
		d[x].s+=d[i].s,wk(i,d[x].w,d[i].w);
	}
	if(dfs(d[n].w,0)!=d[n].x)return 0&printf("-1");
	for(int i=1;i<=n;++i)
		for(int j=he[i];j;j=nx[j])
			printf("%lld %lld\n",i,to[j]);
	return 0;
}