Problem:
Score : 600 points

Problem Statement

We have a tree with N vertices. The i-th edge connects Vertex A_i and B_i bidirectionally.

Takahashi is standing at Vertex u, and Aoki is standing at Vertex v.

Now, they will play a game of tag as follows:

1. If Takahashi and Aoki are standing at the same vertex, the game ends. Otherwise, Takahashi moves to a vertex of his choice that is adjacent to his current vertex.

2. If Takahashi and Aoki are standing at the same vertex, the game ends. Otherwise, Aoki moves to a vertex of his choice that is adjacent to his current vertex.

3. Go back to step 1.

Takahashi performs his moves so that the game ends as late as possible, while Aoki performs his moves so that the game ends as early as possible.

Find the number of moves Aoki will perform before the end of the game if both Takahashi and Aoki know each other's position and strategy.

It can be proved that the game is bound to end.

Constraints

2 \leq N \leq 10^5

1 \leq u,v \leq N

u \neq v

1 \leq A_i,B_i \leq N

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N u v
A_1 B_1
:
A_{N-1} B_{N-1}

Output

Print the number of moves Aoki will perform before the end of the game.

Sample Input 1

5 4 1
1 2
2 3
3 4
3 5

Sample Output 1

2

If both players play optimally, the game will progress as follows:

Takahashi moves to Vertex 3.

Aoki moves to Vertex 2.

Takahashi moves to Vertex 5.

Aoki moves to Vertex 3.

Takahashi moves to Vertex 3.

Here, Aoki performs two moves.

Note that, in each move, it is prohibited to stay at the current vertex.

Sample Input 2

5 4 5
1 2
1 3
1 4
1 5

Sample Output 2

1

Sample Input 3

2 1 2
1 2

Sample Output 3

0

Sample Input 4

9 6 1
1 2
2 3
3 4
4 5
5 6
4 7
7 8
8 9

Sample Output 4

5

Solution in Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::cmp::{Ordering};

#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};

#[allow(unused_imports)]
use std::iter::FromIterator;

#[allow(unused_macros)]
macro_rules! min {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::min($x, min!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! max {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::max($x, max!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! get { 
    ([$t: ty]) => { 
        { 
            let mut line = String::new(); 
            stdin().read_line(&mut line).unwrap(); 
            line.split_whitespace().map(|t|t.parse::<$t>().unwrap()).collect::<Vec<_>>()
        }
    };
    ([$t: ty];$n: expr) => {
        (0..$n).map(|_|get!([$t])).collect::<Vec<_>>()
    };
    ($t: ty) => {
        {
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t: ty),*) => {
        { 
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*)
        }
    };
    ($t: ty; $n: expr) => {
        (0..$n).map(|_|get!($t)).collect::<Vec<_>>()
    };
    ($($t: ty),*; $n: expr) => {
        (0..$n).map(|_|get!($($t),*)).collect::<Vec<_>>()
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*).unwrap();
    }
}

const BIG_STACK_SIZE: bool = true;

#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}

fn dfs(node: usize, nodes: &Vec<Vec<usize>>, depth: &mut Vec<usize>, visited: &mut Vec<bool>, current_depth: usize) {
    visited[node] = true;
    for &next in &nodes[node] {
        if visited[next] {
            continue;
        }
        dfs(next, nodes, depth, visited, current_depth+1);
        visited[next] = true;
    }
    depth[node] = current_depth;
}

fn dfs2(node: usize, nodes: &Vec<Vec<usize>>, visited: &mut Vec<bool>, goal: usize) -> Option<usize> {
    visited[node] = true;
    if node == goal {
        return Some(0);
    }
    for &next in &nodes[node] {
        if visited[next] {
            continue;
        }
        let depth = dfs2(next, nodes, visited, goal);
        visited[next] = true;
        if let Some(depth) = depth {
            return Some(depth+1);
        }
    }
    None
}

fn lower_bound<F>(l: usize, r: usize, criterion: F) -> usize
where
    F: Fn(usize) -> bool,
{
    let mut l = l;
    let mut r = r;
    while r - l > 1 {
        let mid = l + (r - l) / 2;
        if criterion(mid) {
            r = mid;
        } else {
            l = mid;
        }
    }
    l
}

fn solve() {
    let (n,u,v) = get!(usize, usize, usize);
    let ab = get!(usize, usize; n-1);

    if u == v {
        println!("0");
        return;
    }

    let mut nodes = vec![Vec::new(); n+1];
    for (a,b) in ab {
        nodes[a].push(b);
        nodes[b].push(a);
    }

    let mut a_depth = vec![0; n+1];
    let mut t_depth = vec![0; n+1];
    dfs(u, &nodes, &mut t_depth, &mut vec![false; n+1], 0);
    dfs(v, &nodes, &mut a_depth, &mut vec![false; n+1], 0);

    let mut a_depth_inv = BTreeMap::new();
    let mut t_depth_inv = BTreeMap::new();
    for i in 1..n+1 {
        a_depth_inv.entry(&a_depth[i]).or_insert(Vec::new()).push(i);
        t_depth_inv.entry(&t_depth[i]).or_insert(Vec::new()).push(i);
    }

    let mn = dfs2(u, &nodes, &mut vec![false; n+1], v).unwrap();

    let crit = |dist: usize| {
        let vec = a_depth_inv.get(&dist).cloned().unwrap_or(Vec::new());
        for node in vec {
            if t_depth[node] <= dist {
                return false;
            }
        }
        true
    };
    let res = lower_bound(mn, n, crit);
    println!("{}", res-1);
}