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 <utility>
#include <queue>
#include <vector>
#include <stack>
#include <list>
#include <map>
#include <set>
#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstdint>
#include <cstring>
#include <cmath>

using namespace std;

typedef long long ll;

int main() {
	int X, Y, E;
	cin >> X >> Y >> E;
	int c[202][202] = { {0} };
	for (int i = 0; i < E; i++) {
		int x, y;
		cin >> x >> y;
		c[x + 1][y + 101] = 1;
	}
	for (int i = 0; i < X; i++) c[0][i + 1] = 1;
	for (int i = 0; i < Y; i++) c[i + 101][201] = 1;
	int frm[202];
	queue<int> q;
	int r = 0;
	while (true) {
		for (auto& e : frm)e = -1;
		frm[0] = 0;
		q.push(0);
		while (!q.empty()) {
			int f = q.front();
			q.pop();
			for (int i = 0; i < 202; i++) {
				if (c[f][i] > 0 && frm[i] == -1){
					frm[i] = f;
					q.push(i);
				}
			}
		}
		if (frm[201] == -1)break;
		int z = INT32_MAX / 2,s = 201,t;
		while (s != 0) {
			t = frm[s];
			z = min(z, c[t][s]);
			s = t;
		}
		r += z;
		s = 201;
		while (s != 0) {
			t = frm[s];
			c[t][s] -= z;
			c[s][t] += z;
			s = t;
		}
	}
	cout << r << endl;
}