Blockade

The internet of Bytotia is a network of servers joined by one-way links. An attacker wants to cut off every route from server 1 to server $n$. The attacker can plant a trap on any link, and when a trap goes off it destroys the single link it sits on. The attacker uses as few traps as possible while still guaranteeing that no message can travel from server 1 to server $n$. Find that minimum number of traps.

The first line contains two integers $n$ and $m$ ($2 \le n \le 10000$): the number of servers and the number of links. Servers are numbered from $1$ to $n$. Each of the next $m$ lines contains two integers $a$ and $b$ ($1 \le a, b \le n$, $a \ne b$), describing a one-way link from server $a$ to server $b$. There is at most one direct link between any two servers.

Print a single integer: the minimum number of links that must be destroyed so that server 1 can no longer reach server $n$.