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<iostream>
#include<cstdio>
#include<map>
#include<algorithm>
#define FOR(i,a,b) for(int i=a;i<=b;i++)
using namespace std;
typedef long long ll;
const int N=200200;
int n,u,o[N],sz[N],fa[N];
ll t,a[N],su[N];
map<ll,int>h;
bool cmp(int x,int y){return a[x]>a[y];}
int main(){
	scanf("%d",&n);
	FOR(i,1,n) scanf("%lld",&a[i]),h[a[i]]=o[i]=i,sz[i]=1;
	sort(o+1,o+n+1,cmp);
	FOR(i,1,n-1){
		u=o[i];t=a[u]+2*sz[u]-n;
		if(!h.count(t) || h[t]==u || fa[h[t]]) return puts("-1"),0;
		sz[fa[u]=h[t]]+=sz[u];
		su[fa[u]]+=su[u]+sz[u];
	}
	if(su[o[n]]!=a[o[n]]) return puts("-1"),0;
	FOR(i,1,n)if(fa[i]) cout<<i<<' '<<fa[i]<<'\n';
}