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 <algorithm>
#include <map>
#define MN 101000

typedef long long ll;

struct xxx{
	ll d;
	int id;
}a[MN];

int siz[MN];
std::map<ll, int> mp;
int x[MN], y[MN];

bool cmp(xxx a, xxx b) {return a.d < b.d;}

int main()
{
	int n; scanf("%d", &n);
	for(int i = 1; i <= n; i++) scanf("%lld", &a[i].d), a[i].id = i;
	std::sort(a + 1, a + n + 1, cmp);
	for(int i = 1; i <= n; i++) mp[a[i].d] = i, siz[i] = 1;
	ll sum = 0;
	for(int i = n; i >= 2; i--)
	{
		sum += siz[i];
		a[i].d -= n - 2 * siz[i]; 
		if(!mp[a[i].d] || mp[a[i].d] >= i) return 0 * puts("-1");
		siz[mp[a[i].d]] += siz[i];
		x[n - i + 1] = a[i].id; y[n - i + 1] = a[mp[a[i].d]].id; 
	}
	if(sum != a[1].d) return 0 * puts("-1");
	for(int i = 1; i < n; i++) printf("%d %d\n", x[i], y[i]);
}