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 <algorithm>
#include <iostream>
#include <cstdio>
#define mp make_pair
#define fi first
#define se second
using namespace std;
pair <long long, int> a[1000006];
pair <int, int> edge[1000006];
int sze[1000006];
int main(){
	int n;
	cin >> n;
	for (int i = 1; i <= n; ++ i){
		scanf("%lld", &a[i].fi);
		a[i].se = i;
	}
	sort(a + 1, a + 1 + n);
	int m = 0;
	long long sum = 0;
	for (int i = n; i >= 2; -- i){
		sum += ++ sze[i];
		long long d = a[i].fi - n + 2 * sze[i];
		int index = lower_bound(a + 1, a + 1 + n, mp(d, 0)) - a;
		if (a[index].fi != d || index >= i){
			cout << -1 << endl;
			return 0;
		}
		edge[++ m] = mp(a[index].se, a[i].se);
		sze[index] += sze[i];
	}
	if (a[1].fi != sum){
		cout << -1 << endl;
		return 0;
	}
	for (int i = 1; i <= m; ++ i)
		printf("%d %d\n", edge[i].fi, edge[i].se);
	return 0;
}
/*
7
9
14
12
17
10
13
18
*/