Reachability from the Capital

题目描述

There are $n$ cities and $m$ roads in Berland. Each road connects a pair of cities. The roads in Berland are one-way.

What is the minimum number of new roads that need to be built to make all the cities reachable from the capital?

New roads will also be one-way.

输入格式

The first line of input consists of three integers $n$ , $m$ and $s$ ( $1 \le n \le 5000, 0 \le m \le 5000, 1 \le s \le n$ ) — the number of cities, the number of roads and the index of the capital. Cities are indexed from $1$ to $n$ .

The following $m$ lines contain roads: road $i$ is given as a pair of cities $u_i$ , $v_i$ ( $1 \le u_i, v_i \le n$ , $u_i \ne v_i$ ). For each pair of cities $(u, v)$ , there can be at most one road from $u$ to $v$ . Roads in opposite directions between a pair of cities are allowed (i.e. from $u$ to $v$ and from $v$ to $u$ ).

输出格式

Print one integer — the minimum number of extra roads needed to make all the cities reachable from city $s$ . If all the cities are already reachable from $s$ , print 0.

输入输出样例

输入样例 #1

9 9 1
1 2
1 3
2 3
1 5
5 6
6 1
1 8
9 8
7 1

输出样例 #1

3

输入样例 #2

5 4 5
1 2
2 3
3 4
4 1

输出样例 #2

1

说明/提示

The first example is illustrated by the following:

For example, you can add roads ( $6, 4$ ), ( $7, 9$ ), ( $1, 7$ ) to make all the cities reachable from $s = 1$ .

The second example is illustrated by the following:

In this example, you can add any one of the roads ( $5, 1$ ), ( $5, 2$ ), ( $5, 3$ ), ( $5, 4$ ) to make all the cities reachable from $s = 5$ .