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;

const int N = 100010;

typedef long long LL;

LL D[N]; int id[N], sz[N];
map<LL, int> mp;

inline void Fuck() {
	puts("-1"), exit(0);
}

vector<int> G[N];

inline void adde(int from, int to) {
	G[from].push_back(to), G[to].push_back(from);
}

LL dfs(int u, int f) {
	LL res = 0;
	for (auto v : G[u]) if (v != f) 
		res += dfs(v, u) + sz[v];
	return res;
}

int main() {
	int n; scanf("%d", &n);
	for (int i = 1; i <= n; i++) scanf("%lld", &D[i]), mp[D[i]] = i, sz[i] = 1, id[i] = i;
	sort(id + 1, id + n + 1, [](int a, int b){return D[a] > D[b];});
	for (int i = 1; i < n; i++) {
		int v = id[i];
		LL tmp = D[v] - n + sz[v] * 2;
		if (!mp.count(tmp) || tmp >= D[v]) Fuck();
		adde(v, mp[tmp]), sz[mp[tmp]] += sz[v];
	}
	if (dfs(id[n], 0) != D[id[n]]) Fuck();
	for (int i = 1; i <= n; i++)
		for (auto v : G[i]) if (v > i) printf("%d %d\n", i, v);
}