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 <algorithm>

using i64 = long long;

const int N = 100000 + 7;

int n;
int s[N], e[N];
i64 d[N], t;
int u[N], v[N];

int main() {
//	freopen("code.in", "r", stdin);
//	freopen("code.out", "w", stdout);

	scanf("%d", &n);
	for (int i = 1; i <= n; ++i)
		scanf("%lld", d + i), e[i] = i, s[i] = 1;
	std::sort(e + 1, e + n + 1, [](int a, int b) {
		return d[a] < d[b];
	});
	for (int i = n; i > 1; --i) {
		int j = std::lower_bound(e + 1, e + n + 1, d[e[i]] - n + s[e[i]] * 2, [](int a, i64 b) {
			return d[a] < b;
		}) - e;
		if (d[e[j]] != d[e[i]] - n + s[e[i]] * 2) return printf("-1"), 0;
		s[e[j]] += s[e[i]], t += s[e[i]];
		u[i] = e[i], v[i] = e[j];
	}
	if (d[e[1]] != t) return printf("-1"), 0;
	for(int i = 2; i <= n; i++)
		printf("%d %d\n", u[i], v[i]);
	return 0;
}