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;

#define int long long
#define F first
#define S second
const int MN = 101234;

int sz[MN], par[MN], sum[MN];
pair <int, int> d[MN];

int32_t main() {
	int n;
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> d[i].F;
		d[i].S = i;
	}
	for (int i = 0; i < n; i++)
		sz[i] = 1;
	sort(d, d + n);
	for (int i = n - 1; i >= 1; i--) {
//		cerr << d[i].F << ' ' << d[i].F - n + 2 * sz[i] << endl;
		int pr = lower_bound(d, d + n, (pair <int, int>){d[i].F - n + 2 * sz[i], 0ll}) - d;
		if (pr >= i || pr == n || d[pr].F != d[i].F - n + 2 * sz[i])
			return cout << -1, 0;
		sz[pr] += sz[i];
		sum[pr] += sum[i] + sz[i];
		par[d[i].S] = d[pr].S;
	}
	if (sum[0] != d[0].F)
		return cout << -1, 0;
	for (int i = 1; i < n; i++)
		cout << par[d[i].S] + 1 << ' ' << d[i].S + 1 << endl;
}