Delivery robots

Juku likes hot dogs. A lot.

Juku lives in a town with $V$ intersections and $E$ two-way streets connecting them. The intersections are numbered $1 \ldots V$. No pair of intersections is connected by more than one street, and no street connects an intersection to itself. From every intersection, it is possible to reach every other intersection along the streets. Each intersection has a hot dog stand.

Juku is building delivery robots to bring him hot dogs. He chooses two intersections, the initial location of the robots $s$ and his own location $f$, and programs the robots so that he gets hot dogs from as many different stands as possible.

Programming the robots is limited. Each robot can store an array $n$ and a variable $b$. A robot starts moving from intersection $s$ and repeats these steps:

1. If the robot is at intersection $b$, it buys a hot dog from the stand there.
2. If the robot is at intersection $f$, it gives the hot dog to Juku and stops.
3. The robot moves to intersection $n[i]$, where $i$ is its current location.

For every $i \in 1 \ldots V$, there must be a street between intersections $i$ and $n[i]$. Otherwise the robot crashes.

Find the maximum number of different stands Juku can get hot dogs from, when he chooses $s$ and $f$ optimally and enters $n$ and $b$ into the robots optimally. The values $s$ and $f$ are the same for all robots, but $n$ and $b$ can differ for each robot. You may assume Juku can use arbitrarily many robots.

The first line contains two integers $V$ and $E$, the number of intersections and the number of streets ($1 \le V \le 10^5$, $1 \le E \le 3 \cdot 10^5$). Each of the next $E$ lines contains two integers $u$ and $v$, meaning there is a street between intersections $u$ and $v$.

Print a single integer: the maximum number of different stands Juku can get hot dogs from.