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>
#define PB push_back
#define MP std::make_pair
#define FI first
#define SE second
#define M 1000005
#define INF 1000000000
typedef long long ll;
ll n,D[M],size[M],sum;
std::multiset <std::pair <ll,ll> > Set;
std::pair <ll,ll> Edge[M];
ll read(){
	char c=getchar();ll ans=0;
	while (c<'0'||c>'9') c=getchar();
	while (c>='0'&&c<='9') ans=ans*10+c-'0',c=getchar();
	return ans;
}
void Write(ll x){
	if (x<10) putchar(x+'0');
	else Write(x/10),putchar(x%10+'0');
	return;
}
int main(){
	n=read();
	for (ll i=1;i<=n;i++) size[i]=1,Set.insert(MP(D[i]=read(),i));
	for (ll i=1;i<n;i++){
		auto it=Set.end();--it;ll X=it->FI,Y=it->SE;Set.erase(it);
		auto nxt=Set.lower_bound(MP(X+size[Y]-(n-size[Y]),0));
		if (nxt==Set.end()||nxt->FI>X+size[Y]-(n-size[Y])) return !printf("-1");
		Edge[i]=MP(Y,nxt->SE),size[nxt->SE]+=size[Y]; 
	}
	for (int i=1;i<=n;i++) sum+=size[i]-1;
	if (sum!=Set.begin()->FI) return !printf("-1");
	for (int i=1;i<n;i++) Write(Edge[i].FI),putchar(' '),Write(Edge[i].SE),putchar('\n');
	return 0;
}