Problem: A bipartite graph G = (V, E) is a graph in which the vertex set V can be divided into two disjoint subsets X and Y such that every edge e ∈ E has one end point in X and the other end point in Y.

A matching M is a subset of edges such that each node in V appears in at most one edge in M.

Given a bipartite graph, find the size of the matching which has the largest size.

Constraints

* 1 ≤ |X|, |Y| ≤ 100
* 0 ≤ |E| ≤ 10,000

Input


|X| |Y| |E|
x0 y0
x1 y1
:
x|E|-1 y|E|-1


|X| and |Y| are the number of vertices in X and Y respectively, and |E| is the number of edges in the graph G. The vertices in X are named with the numbers 0, 1,..., |X|-1, and vertices in Y are named with the numbers 0, 1,..., |Y|-1, respectively.

xi and yi are the node numbers from X and Y respectevely which represent the end-points of the i-th edge.

Output

Print the largest size of the matching.

Example

Input

3 4 6
0 0
0 2
0 3
1 1
2 1
2 3


Output

3

Solution (in CPP):

Solution:
#include <iostream>
#include <vector>
using namespace std;

int A, B, E, match[5009]; vector<int> G[5009];
bool used[5009];

bool dfs(int pos) {
	used[pos] = true;
	for (int i = 0; i < G[pos].size(); i++) {
		if (match[G[pos][i]] < 0 || (used[match[G[pos][i]]] == false && dfs(match[G[pos][i]]) == true)) {
			match[pos] = G[pos][i];
			match[G[pos][i]] = pos;
			return true;
		}
	}
	return false;
}

int main() {
	cin >> A >> B >> E;
	for (int i = 0; i < E; i++) {
		int p1, p2; cin >> p1 >> p2;
		G[p1].push_back(p2 + A);
		G[p2 + A].push_back(p1);
	}
	for (int i = 0; i < A + B; i++) match[i] = -1;

	int cnt = 0;
	for (int i = 0; i < A + B; i++) {
		if (match[i] >= 0) continue;
		for (int j = 0; j < A + B; j++) used[j] = false;
		bool I = dfs(i);
		if (I == true) cnt++;
	}
	cout << cnt << endl;
	return 0;
}