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)

use std::io::{self, BufRead, BufWriter, Write};

fn solve<R, W>(reader: R, mut writer: W)
where
    R: BufRead,
    W: Write,
{
    let mut lines = reader.lines();
    let _ = lines.next().unwrap().unwrap();
    let table: Vec<Vec<bool>> = lines.map(|s| {
        s.unwrap().chars().map(|c| c == '1').collect()
    }).collect();

    let mut ans = -1;
    for i in 0..table.len() {
        let group = max_group(&table, i);
        if group > ans {
            ans = group;
        }
    }

    writeln!(&mut writer, "{}", ans).unwrap();
}

fn max_group(table: &[Vec<bool>], start: usize) -> i32 {
    let mut queue: Vec<usize> = vec![start];
    let mut done: Vec<i32> = vec![0;table.len()];
    done[start] = 1; // group 1
    let mut count: i32 = 1; // start

    let mut gr: i32 = 0;
    while ! queue.is_empty() {
        let x = queue.remove(0);
        gr = done[x];
        for i in 0 .. table.len() {
            if ! table[x][i] {
                continue;
            }

            if done[i] == 0 {
                // new node
                count += 1;
                queue.push(i);
                done[i] = gr + 1;
            } else if done[i] != gr + 1 && done[i] != gr - 1 {
                // failed
                return -1;
            }
        }
    }

    gr
}


fn main() {
    let stdio = io::stdin();
    let input = stdio.lock();

    let stdout = io::stdout();
    let output = BufWriter::new(stdout.lock());

    solve(input, output);
}

#[cfg(test)]
mod tests {
    use super::*;

    const TESTS: &'static [(&'static [u8], &'static [u8])] = &[
        (
            br"2
01
10", br"2
",
        ),
        (
            br"3
011
101
110", br"-1
",
        ),
        (
            br"6
010110
101001
010100
101000
100000
010000", br"4
",
        ),
    ];

    #[test]
    fn test_b() {
        for &(input, expected) in TESTS {
            let mut output = Vec::new();
            solve(input, &mut output);
            let expected_str = String::from_utf8(expected.to_vec()).unwrap();
            let output_str = String::from_utf8(output).unwrap();
            assert_eq!(expected_str, output_str);
        }
    }
}