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;
use std::cmp;
use std::collections::BinaryHeap;
use std::collections::HashMap;
use std::collections::HashSet;
use std::f64::consts::PI;

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf
}


fn main() {
    let n: usize = read_line().trim().parse().unwrap();
    let mut graph = vec![Vec::new(); n];
    for i in 0..n {
        let line: Vec<bool> = read_line().trim().chars().map(|c| c == '1').collect();
        for j in 0..n {
            if line[j] {
                graph[i].push(j);
            }
        }
    }

    let mut ans = -1;
    for i in 0..n {
        let mut visited = vec![false; n];
        let mut prev = HashSet::new();
        let mut current = HashSet::new();
        let mut k = 0;
        current.insert(i);

        loop {
            if current.is_empty() {
                break;
            }
            let mut next = HashSet::new();
            let mut valid = true;
            for v in current.iter() {
                visited[*v] = true;
            }
            for v in current.iter() {
                for w in graph[*v].iter() {
                    if prev.contains(w) {
                        continue;
                    }
                    if visited[*w] {
                        valid = false;
                        break;
                    }
                    next.insert(*w);
                }
            }
            if valid {
                k += 1;
                prev = current.clone();
                current = next.clone();
            } else {
                k = -1;
                break;
            }
        }
        let valid = visited.iter().find(|b| !**b).is_none();
        if valid {
            ans = cmp::max(ans, k);
        }
    }
    println!("{}", ans);
}