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>

void bye() { std::cout << -1 << std::endl; exit(0); }
const int MAXN = 100010;
typedef long long LL;
std::map<LL, LL> idx, sub, fa, dep;
int n;
LL D[MAXN];
int main() {
	std::ios_base::sync_with_stdio(false), std::cin.tie(0);
	std::cin >> n;
	for (int i = 1; i <= n; ++i)
		std::cin >> D[i], idx[D[i]] = i, sub[D[i]] = 1;
	std::sort(D + 1, D + 1 + n);
	for (int i = n; i > 1; --i) {
		LL td = D[i] - n + sub[D[i]] * 2;
		if (td >= D[i] || !idx.count(td)) bye();
		sub[td] += sub[D[i]];
		fa[D[i]] = td;
	}
	for (int i = 2; i <= n; ++i) {
		dep[D[i]] = dep[fa[D[i]]] + 1;
		D[1] -= dep[D[i]];
	}
	if (D[1]) bye();
	for (int i = 2; i <= n; ++i)
		std::cout << idx[fa[D[i]]] << ' ' << idx[D[i]] << '\n';
	return 0;
}