Description

Input

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 $u$).

Output

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.

9 9 1<br>1 2<br>1 3<br>2 3<br>1 5<br>5 6<br>6 1<br>1 8<br>9 8<br>7 1<br>

5 4 5<br>1 2<br>2 3<br>3 4<br>4 1<br>

3<br>

1<br>

Note

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 $s = 5$.