二分图最大匹配 - Problem

#898. 二分图最大匹配

Statistics

给定一张二分图，二分图的左部点编号为 $1 \sim L$，右部点编号为 $1 \sim R$。

有 $M$ 条边，第 $i$ 条边连接连接了左侧第 $a_i$ 个点与右侧第 $b_i$ 个点。

找出该二分图的一个最大匹配。

输入格式

输入的第一行包含三个整数 $L$, $R$, $M$。

接下来 $M$ 行，每行两个整数 $a_i, b_i$，描述一条边。图中可能存在重边。

输出格式

输出的第一行包含一个整数 $k$，表示最大匹配的大小。

接下来 $K$ 行，每行两个整数 $c_i$, $d_i$，表示将左侧第 $c_i$ 个点匹配到右侧第 $d_i$ 个点。

如果有多种合法方案，你可以输出任意一种。

样例数据

样例输入

样例输出

2
1 1
3 2

子任务

对于所有数据，$1 \le L, R \le 2 \cdot 10^5$，$1 \le M \le 6 \cdot 10^5$，$1 \le a_i \le L$，$1 \le b_i \le R$。

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