Problem:
Score : 800 points

Problem Statement

Takahashi and Aoki will play a game on a tree.
The tree has N vertices numbered 1 to N, and the i-th of the N-1 edges connects Vertex a_i and Vertex b_i.

At the beginning of the game, each vertex contains a coin.
Starting from Takahashi, he and Aoki will alternately perform the following operation:

Choose a vertex v that contains one or more coins, and remove all the coins from v.

Then, move each coin remaining on the tree to the vertex that is nearest to v among the adjacent vertices of the coin's current vertex.

The player who becomes unable to play, loses the game.
That is, the player who takes his turn when there is no coin remaining on the tree, loses the game.
Determine the winner of the game when both players play optimally.

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq a_i, b_i \leq N

a_i \neq b_i

The graph given as input is a tree.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
a_2 b_2
:
a_{N-1} b_{N-1}

Output

Print First if Takahashi will win, and print Second if Aoki will win.

Sample Input 1

3
1 2
2 3

Sample Output 1

First

Here is one possible progress of the game:

Takahashi removes the coin from Vertex 1. Now, Vertex 1 and Vertex 2 contain one coin each.

Aoki removes the coin from Vertex 2. Now, Vertex 2 contains one coin.

Takahashi removes the coin from Vertex 2. Now, there is no coin remaining on the tree.

Aoki takes his turn when there is no coin on the tree and loses.

Sample Input 2

6
1 2
2 3
2 4
4 6
5 6

Sample Output 2

Second

Sample Input 3

7
1 7
7 4
3 4
7 5
6 3
2 1

Sample Output 3

First

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

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::{Write, BufWriter};
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, [ $t:tt ]) => {{
        let len = read_value!($next, usize);
        (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    }};

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused)]
macro_rules! debug {
    ($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap());
}
#[allow(unused)]
macro_rules! debugln {
    ($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap());
}

/**
 * Manages a tree and calculates the diameter of it.
 * Verified by: NJPC 2017-E
 *              (http://njpc2017.contest.atcoder.jp/submissions/1089492)
 */
struct Diameter {
    n: usize,
    edges: Vec<Vec<(usize, i64)>>,
    x: usize,
    y: usize,
}

impl Diameter {
    fn dfs(&self, v: usize, dist: &mut [i64], p: Option<usize>, d: i64) {
        dist[v] = d;
        for &(w, c) in self.edges[v].iter() {
            if Some(w) == p { continue; }
            self.dfs(w, dist, Some(v), d + c);
        }
    }
    pub fn new(n: usize) -> Self {
        Diameter {
            n: n,
            edges: vec![Vec::new(); n],
            x: n,
            y: n,
        }
    }
    pub fn add_edge(&mut self, a: usize, b: usize, c: i64) {
        self.edges[a].push((b, c));
        self.edges[b].push((a, c));
    }
    pub fn diameter(&mut self) -> (usize, usize) {
        let n = self.n;
        if self.x < n {
            return (self.x, self.y);
        }
        // farthest from 0
        let mut dist = vec![-1; n];
        self.dfs(0, &mut dist, None, 0);
        let mut maxi = 0;
        for i in 1 .. n {
            if dist[maxi] < dist[i] {
                maxi = i;
            }
        }
        self.x = maxi;
        // farthest from x
        self.dfs(maxi, &mut dist, None, 0);
        let mut maxi = 0;
        for i in 0 .. n {
            if dist[maxi] < dist[i] {
                maxi = i;
            }
        }
        self.y = maxi;
        (self.x, self.y)
    }
    pub fn farthest(&mut self) -> Vec<i64> {
        let n = self.n;
        if self.x >= n {
            self.diameter();
        }
        let mut ret = vec![0; n];
        let mut tmp = vec![-1; n];
        /* For every vertex, the farthest point from it is either x or y. */
        self.dfs(self.x, &mut ret, None, 0);
        self.dfs(self.y, &mut tmp, None, 0);
        for i in 0 .. n {
            ret[i] = max(ret[i], tmp[i]);
        }
        ret
    }
}

fn solve() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {
        ($($format:tt)*) => (write!(out,$($format)*).unwrap());
    }
    input! {
        n: usize,
        ab: [(usize1, usize1); n - 1],
    }
    let mut diam = Diameter::new(n);
    for &(a, b) in &ab {
        diam.add_edge(a, b, 1);
    }
    let (x, _y) = diam.diameter();
    let far = diam.farthest();
    let d = far[x] as usize + 1;
    let mut dp = vec![false; d + 1];
    for i in 1..d + 1 {
        let mut win = !dp[i - 1];
        if i >= 3 && !dp[i - 2] {
            win = true;
        }
        dp[i] = win;
    }
    puts!("{}\n", if dp[d] { "First" } else { "Second" });
}

fn main() {
    // In order to avoid potential stack overflow, spawn a new thread.
    let stack_size = 104_857_600; // 100 MB
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(|| solve()).unwrap().join().unwrap();
}