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)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn dfs(start: usize, graph: &Vec<Vec<usize>>, cur_color: i32, color: &mut Vec<i32>) -> bool {
    if color[start] != 0 {
        return cur_color == color[start];
    }
    color[start] = cur_color;
    for &to in graph[start].iter() {
        if !dfs(to, &graph, -1 * cur_color, color) {
            return false;
        }
    }
    true
}

fn is_biparate(graph: &Vec<Vec<usize>>) -> bool {
    let mut color = vec![0; graph.len()];
    for i in 0..graph.len() {
        if color[i] == 0 {
            if !dfs(i, graph, 1, &mut color) {
                return false;
            }
        }
    }
    true
}

const INF: i64 = 1000000;

fn main() {
    let n = read::<usize>();
    let mut graph = vec![vec![]; n];
    let mut edges = vec![vec![INF; n]; n];
    for i in 0..n {
        let s = read::<String>().chars().collect::<Vec<_>>();
        for j in 0..n {
            if s[j] == '1' {
                graph[i].push(j);
                edges[i][j] = 1;
            }
        }
    }

    if !is_biparate(&graph) {
        println!("-1");
        return;
    }

    let mut ans = 0;
    warshall_floyd(n, &mut edges);
    for i in 0..n {
        for j in i + 1..n {
            ans = max(edges[i][j], ans);
        }
    }
    println!("{}", ans + 1);
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn warshall_floyd(n: usize, edges: &mut Vec<Vec<i64>>) {
    for k in 0..n {
        for i in 0..n {
            for j in 0..n {
                edges[i][j] = std::cmp::min(edges[i][j], edges[i][k] + edges[k][j]);
            }
        }
    }
}