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<bits/stdc++.h>

using namespace std;

const int N = 101;
int X,Y;
int mat[N][N];
bool used[N];
int girls[N];

void add(int x,int y){
    mat[x][y] = 1;
}

int dfs(int v){
    used[v] = true;
    for(int i=0;i<Y;i++){
        if(!mat[v][i]) continue;
        int u = girls[i];
        if(u==-1 || !used[u] && dfs(girls[i])){
            girls[i] = v;
            return 1;
        }
    }
    return 0;
}

int match(){
    int ans = 0;
    memset(girls,-1,sizeof(girls));
    for(int i=0;i<X;i++){
        memset(used,0,sizeof(used));
        ans += dfs(i);
    }
    return ans;
}

int main(){
    int E;
    cin>>X>>Y>>E;
    memset(mat,0,sizeof(mat));
    for(int i=0;i<E;i++){
        int x,y;
        cin>>x>>y;
        add(x,y);
    }

    cout<<match()<<endl;

    return 0;
}