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;

typedef long long ll;

const int MAXN=3e5+7;

ll from[MAXN],to[MAXN];

map<ll,ll> Map;

ll n;
ll a[MAXN],b[MAXN],siz[MAXN],sum[MAXN];

bool cmp(const ll &A,const ll &B){return a[A]>a[B];}
bool cmp2(const ll &A,const ll &B){return A>B;}

ll minn1=1e18,minn2;

int main() {
	cin>>n;
	for(int i=1;i<=n;i++) {
		cin>>a[i];
		b[i]=i;
		Map[a[i]]=i;
		siz[i]=1;
		if(minn1>a[i]) {
			minn1=a[i];
			minn2=i;
		}
	}
	sort(b+1,b+1+n,cmp);
	sort(a+1,a+1+n,cmp2);
	for(ll i=1,i2;i<n;i++) {
		i2=Map[a[i]-abs(n-2*siz[b[i]])];
		if(i2!=0&&a[i]-abs(n-2*siz[b[i]])!=a[i]) {
			siz[i2]+=siz[b[i]];
			sum[i2]+=sum[b[i]]+siz[b[i]];
			from[i]=i2;
			to[i]=b[i];
		}
		else {
			cout<<-1<<endl;
			return 0;
		}
	}
	if(minn1!=sum[minn2]) {
		cout<<-1<<endl;
		return 0;
	}
	for(int i=1;i<n;i++) {
		cout<<from[i]<<" "<<to[i]<<endl;
	}
}