Problem:
Score : 500 points

Problem Statement

Given is a connected undirected graph with N vertices and M edges. The vertices are numbered 1 to N, and the edges are described by a grid of characters S.
If S_{i,j} is 1, there is an edge connecting Vertex i and j; otherwise, there is no such edge.

Determine whether it is possible to divide the vertices into non-empty sets V_1, \dots, V_k such that the following condition is satisfied. If the answer is yes, find the maximum possible number of sets, k, in such a division.

Every edge connects two vertices belonging to two "adjacent" sets. More formally, for every edge (i,j), there exists 1\leq t\leq k-1 such that i\in V_t,j\in V_{t+1} or i\in V_{t+1},j\in V_t holds.

Constraints

2 \leq N \leq 200

S_{i,j} is 0 or 1.

S_{i,i} is 0.

S_{i,j}=S_{j,i}

The given graph is connected.

N is an integer.

Input

Input is given from Standard Input in the following format:

N
S_{1,1}...S_{1,N}
:
S_{N,1}...S_{N,N}

Output

If it is impossible to divide the vertices into sets so that the condition is satisfied, print -1.
Otherwise, print the maximum possible number of sets, k, in a division that satisfies the condition.

Sample Input 1

2
01
10

Sample Output 1

2

We can put Vertex 1 in V_1 and Vertex 2 in V_2.

Sample Input 2

3
011
101
110

Sample Output 2

-1

Sample Input 3

6
010110
101001
010100
101000
100000
010000

Sample Output 3

4

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

#![allow(unused_imports, unused_macros, dead_code)]

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}


macro_rules! ewriteln {
    ($($args:expr),*) => { let _ = writeln!(&mut std::io::stderr(), $($args),*); };
}
macro_rules! trace {
    ($x:expr) => { ewriteln!(">>> {} = {:?}", stringify!($x), $x) };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 1_000_000_007;

#[derive(Debug, Clone)]
enum UF { Root(usize), Child(usize) }

#[derive(Debug)]
struct UnionFind { table: Vec<UF> }
impl UnionFind {

    fn new(n: usize) -> UnionFind {
        UnionFind { table: vec![UF::Root(1); n], }
    }

    fn root(&mut self, x: usize) -> usize {
        match self.table[x] {
            UF::Root(_) => x,
            UF::Child(parent) => {
                let root = self.root(parent);
                self.table[x] = UF::Child(root);
                root
            }
        }
    }

    fn is_same(&mut self, x: usize, y: usize) -> bool {
        self.root(x) == self.root(y)
    }

    fn size(&mut self, x: usize) -> usize {
        let r = self.root(x);
        match self.table[r] {
            UF::Root(size) => size,
            UF::Child(_) => 0
        }
    }

    fn merge(&mut self, x: usize, y: usize) {
        let root_x = self.root(x);
        let root_y = self.root(y);
        if root_x != root_y {
            let size_x = self.size(root_x);
            let size_y = self.size(root_y);
            let (i, j) = if size_x > size_y {
                (root_x, root_y)
            } else {
                (root_y, root_x)
            };
            self.table[i] = UF::Root(size_x + size_y);
            self.table[j] = UF::Child(i);
        }
    }
}

fn is_bipartite_graph(n: usize, g: &Vec<Vec<usize>>) -> bool {
    let mut uf = UnionFind::new(n * 2);
    for i in 0..n {
        for &j in g[i].iter() {
            if i >= j { continue }
            uf.merge(2 * i, 2 * j + 1);
            uf.merge(2 * i + 1, 2 * j);
        }
    }
    for i in 0..n {
        if uf.is_same(2 * i, 2 * i + 1) { return false }
    }
    true
}

fn diameter(n: usize, g: &Vec<Vec<usize>>) -> usize {
    let mut d = vec![vec![n * 2 + 1; n]; n];
    for i in 0..n { d[i][i] = 0 }
    for i in 0..n { for &j in g[i].iter() { d[i][j] = 1; }}
    for k in 0..n {
        for i in 0..n {
            for j in 0..n {
                d[i][j] = min!(d[i][j], d[i][k] + d[k][j]);
            }
        }
    }
    let mut dia = 0;
    for i in 0..n { for j in 0..i { dia = max!(dia, d[i][j]); }}
    dia
}

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let mut g: Vec<Vec<usize>> = vec![vec![]; n];
    for i in 0..n {
        let s: Vec<char> = sc.cin::<String>().chars().collect();
        for j in 0..n {
            if s[j] == '1' {
                g[i].push(j);
            }
        }
    }
    if is_bipartite_graph(n, &g) {
        put!(diameter(n, &g) + 1);
    } else {
        put!(-1);
    }
}

use std::io::{self, Write};
use std::str::FromStr;
use std::collections::VecDeque;

struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
impl Scanner {
    fn new() -> Self { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
}