Problem:
Bipartite Matching

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.

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.

Constraints

1 ≤ |X|, |Y| ≤ 100

0 ≤ |E| ≤ 10,000

Sample Input 1

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

Sample Output 1

3

Solution in C# (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;

namespace No421_1{
    public class Program{
        public static void Main(string[] args){
            var sr = new StreamReader();
            //---------------------------------
            var X = sr.Next<int>();
            var Y = sr.Next<int>();
            var E = sr.Next<int>();

            var bg = new BipartiteGraph(X + Y);
            for(var i = 0; i < E; i++){
                bg.AddEdge(sr.Next<int>(), sr.Next<int>() + X);
            }

            Console.WriteLine(bg.Matching());
            //---------------------------------
        }
    }

    public class BipartiteGraph{
        private readonly List<int>[] _adj;
        private readonly int[] _match;
        private readonly bool[] _used;
         
        public BipartiteGraph(int v){
            _adj = new List<int>[v];
            for(var i = 0; i < v; i++) _adj[i] = new List<int>();
            _match = new int[v];
            _used = new bool[v];
        }

        public void AddEdge(int u, int v){
            _adj[u].Add(v);
            _adj[v].Add(u);
        }

        public int Matching(){
            var res = 0;
            for(var i = 0; i < _match.Length; i++) _match[i] = -1;
            for(var v = 0; v < _match.Length; v++){
                if(_match[v] < 0){
                    for(var j = 0; j < _used.Length; j++) _used[v] = false;
                    if(Dfs(v)) res++;
                }
            }
            return res;
        }

        private bool Dfs(int v){
            _used[v] = true;
            for(var i = 0; i < _adj[v].Count; i++){
                var u = _adj[v][i];
                var w = _match[u];
                if(w < 0 || !_used[w] && Dfs(w)){
                    _match[v] = u;
                    _match[u] = v;
                    return true;
                }
            }
            return false;
        }
    }

    public class StreamReader{
        private readonly char[] _c = {' '};
        private int _index = -1;
        private string[] _input = new string[0];
        private readonly System.IO.StreamReader _sr = new System.IO.StreamReader(Console.OpenStandardInput());

        public T Next<T>(){
            if(_index == _input.Length - 1){
                _index = -1;
                while(true){
                    string rl = _sr.ReadLine();
                    if(rl == null){
                        if(typeof(T).IsClass) return default(T);
                        return (T)typeof(T).GetField("MinValue").GetValue(null);
                    }
                    if(rl != ""){
                        _input = rl.Split(_c, StringSplitOptions.RemoveEmptyEntries);
                        break;
                    }
                }
            }
            return (T)Convert.ChangeType(_input[++_index], typeof(T), System.Globalization.CultureInfo.InvariantCulture);
        }

        public T[] Next<T>(int x){
            var ret = new T[x];
            for(var i = 0; i < x; ++i) ret[i] = Next<T>();
            return ret;
        }

        public T[][] Next<T>(int y, int x){
            var ret = new T[y][];
            for(var i = 0; i < y; ++i) ret[i] = Next<T>(x);
            return ret;
        }
    }
}