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: Wrong Answer)

use std::io::{stdin, Read};

macro_rules! parse {
    ($it: ident) => {
        $it.next().unwrap().parse().unwrap()
    };
    ($it: ident,2) => {
        (parse!($it), parse!($it))
    };
    ($it: ident,3) => {
        (parse!($it), parse!($it), parse!($it))
    };
    ($it: ident,4) => {
        (parse!($it), parse!($it), parse!($it), parse!($it))
    };
    ($it: ident, $n: ident) => {
        (&mut $it).take($n).map(|e| e.parse().unwrap()).collect();
    };
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    let mut it = s.split_whitespace();
    let n = parse!(it);
    let g = (0..n)
        .map(|_| {
            it.next()
                .unwrap()
                .chars()
                .enumerate()
                .filter(|&(i, x)| x.to_digit(2).unwrap() != 0)
                .map(|(i, x)| i)
                .collect::<Vec<usize>>()
        })
        .collect::<Vec<_>>();
    let mut color: Vec<Option<usize>> = vec![None; n];
    if !binary(0, 0, &g, &mut color) {
        println!("{}", -1);
        return;
    }
    let mut d: Vec<Option<usize>> = vec![None; n];
    d[0] = Some(0);
    dfs(0, 1, &g, &mut d);
    let (a, _) = d
        .iter()
        .enumerate()
        .max_by_key(|&(_, &v)| v.unwrap())
        .unwrap();
    let mut d: Vec<Option<usize>> = vec![None; n];
    d[a] = Some(0);
    dfs(a, 1, &g, &mut d);
    let b = d.iter().max().unwrap().unwrap();
    println!("{:?}", b + 1); // DEBUG
}

fn dfs(x: usize, cur: usize, g: &Vec<Vec<usize>>, d: &mut Vec<Option<usize>>) {
    for &y in &g[x] {
        match d[y] {
            Some(_) => {}
            None => {
                d[y] = Some(cur);
                dfs(y, cur + 1, g, d);
            }
        }
    }
}

fn binary(x: usize, c: usize, g: &Vec<Vec<usize>>, color: &mut Vec<Option<usize>>) -> bool {
    for &y in &g[x] {
        if let Some(d) = color[y] {
            if d != c {
                return false;
            }
        } else {
            color[y] = Some(c);
            if !binary(y, 1 - c, &g, color) {
                return false;
            }
        }
    }
    return true;
}