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: Time Limit Exceeded)

//  ____            _                  _                       _       _
// |  _ \ _   _ ___| |_    ___ _ __   | |_ ___ _ __ ___  _ __ | | __ _| |_ ___
// | |_) | | | / __| __|  / __| '_ \  | __/ _ \ '_ ` _ \| '_ \| |/ _` | __/ _ \
// |  _ <| |_| \__ \ |_  | (__| |_) | | ||  __/ | | | | | |_) | | (_| | ||  __/
// |_| \_\\__,_|___/\__|  \___| .__/___\__\___|_| |_| |_| .__/|_|\__,_|\__\___|
//                            |_| |_____|               |_|

//                                                     _        _ _ _____  ___
//                               _ __ ___   __ _ _ __ | |_ __ _/ / |___ / / _ \
//                              | '_ ` _ \ / _` | '_ \| __/ _` | | | |_ \| | | |
//                              | | | | | | (_| | | | | || (_| | | |___) | |_| |
//                              |_| |_| |_|\__,_|_| |_|\__\__,_|_|_|____/ \___/

//https://github.com/manta1130/Competitive_Programming_Template_Rust

#[macro_use]
mod input {

    use std;
    use std::io;

    const SPLIT_DELIMITER: char = ' ';

    #[macro_export]
    #[allow(unused_macros)]
    macro_rules! input {
    ( $($x:expr ),*) => {
        {
            let temp_str = input_line_str();
            let mut split_result_iter = temp_str.split_whitespace();
                $(
                let buf_split_result = split_result_iter.next();
                let buf_split_result = buf_split_result.unwrap();
                    ($x) = buf_split_result.parse().unwrap();
                )*
        }
    };
}

    #[allow(dead_code)]
    pub fn input_line_str() -> String {
        let mut s = String::new();
        io::stdin().read_line(&mut s).unwrap();
        s.trim().to_string()
    }

    #[allow(dead_code)]
    pub fn p<T>(t: T)
    where
        T: std::fmt::Display,
    {
        println!("{}", t);
    }

    #[allow(dead_code)]
    pub fn input_vector2d<T>(line: usize) -> Vec<Vec<T>>
    where
        T: std::str::FromStr,
    {
        let mut v: Vec<Vec<T>> = Vec::new();

        for _ in 0..line {
            let vec_line = input_vector();
            v.push(vec_line);
        }
        v
    }

    #[allow(dead_code)]
    pub fn input_vector<T>() -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v: Vec<T> = Vec::new();

        let s = input_line_str();
        let split_result = s.split(SPLIT_DELIMITER);
        for z in split_result {
            let buf = match z.parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    #[allow(dead_code)]
    pub fn input_vector_row<T>(n: usize) -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::with_capacity(n);
        for _ in 0..n {
            let buf = match input_line_str().parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    pub trait ToCharVec {
        fn to_charvec(&self) -> Vec<char>;
    }

    impl ToCharVec for String {
        fn to_charvec(&self) -> Vec<char> {
            self.to_string().chars().collect::<Vec<_>>()
        }
    }
}

use input::*;
use std::collections::VecDeque;
const INF: usize = 999999999+1;

fn bfs(g: &Vec<Vec<usize>>, e: usize) -> usize {
    let mut q = VecDeque::new();
    let mut table = vec![INF; g.len()];
    q.push_back((e, 0));
    let mut visit=vec![false;g.len()];
    visit[0]=true;

    while !q.is_empty() {
        let pop = q.pop_front().unwrap();
        table[pop.0] = pop.1;
        //println!("from:{:?}",&q);
        for (i,flag) in g[pop.0].iter().enumerate() {
            //println!("f{}:{:?}",i,&q);
            if *flag==0 {
                continue;
            }
            if table[i] == INF{
                q.push_back((i, pop.1 + 1));
                visit[i]=true;
            } else if table[i] % 2 != 0 && pop.1%2 != 0{
                //println!("{:?}->{:?}",&q,pop);
                //println!("{:?},{}:{}",&table,i,e);
                return INF;
            }
            //println!("{}:{:?}",i,&q);
        }
        //println!("after:{:?}",&q);
    }

    //println!("{:?}",&table);
    *table.iter().max().unwrap()
}

fn main() {
    let n: usize;
    input!(n);
    let mut g = vec![];
    for _ in 0..n{
        let a = input_line_str().to_charvec();
        let mut b = vec![];
        for c in a{
            if c=='0'{
                b.push(0);
            }else{
                b.push(1);
            }
        }
        g.push(b);
    }

    let mut ans = 0;
    for i in 0..n {
        ans = std::cmp::max(ans, bfs(&g, i));
    }
    if ans == INF {
        p(-1);
    } else {
        p(ans+1);
    }
}