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 ll long long
const int N=100005;
int n,p[N],sz[N],U[N],V[N];ll tot,d[N];
map<ll,int>mp;vector<int>G[N];
inline bool cmp(int x,int y){return d[x]>d[y];}
void dfs(int x,int d){tot+=d;for(int i=0;i<G[x].size();i++)dfs(G[x][i],d+1);}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%lld",&d[i]),mp[d[i]]=i,sz[i]=1,p[i]=i;
	sort(p+1,p+n+1,cmp);
	for(int i=1;i<n;i++)
	{
		int x=p[i];ll w=d[x]-(n-sz[x])+sz[x];
		if(!mp[w]||w>=d[x]){puts("-1");return 0;}
		int y=mp[w];U[i]=x;V[i]=y;
		sz[y]+=sz[x];G[y].push_back(x);
	}
	dfs(p[n],0);
	if(tot!=d[p[n]]){puts("-1");return 0;}
	for(int i=1;i<n;i++)printf("%d %d\n",U[i],V[i]);
	return 0;
}