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::cmp::{max,min};
fn main() {
    let n = rv::<usize>()[0];
    let mut s = Vec::with_capacity(n);
    for _ in 0..n {
        s.push(rl().trim_right().bytes().map(|x|(x-b'0')as i32).collect::<Vec<_>>());
    }
    for i in 0..n { for j in 0..n { if i!=j && s[i][j]==0 {
        s[i][j]=INF;
    }}}
    for i in 0..n { for j in i+1..n { if s[i][j]==1 {
        for k in j+1..n { if s[i][k]==1 && s[j][k]==1 {
            println!("-1");
            return;
        }}
    }}}
    for k in 0..n { for i in 0..n { for j in 0..n {
        s[i][j]=min(s[i][j],s[i][k]+s[k][j]);
    }}}
    let mut d = vec![0;n];
    for i in 0..n {
        let mut p=i;
        for j in 0..i { if s[i][j]<INF {
            p=j;
            break;
        }}
        for j in i..n { if s[i][j]<INF {
            d[p]=max(d[p],s[i][j]+1);
        }}
    }
    println!("{}",d.into_iter().sum::<i32>());
}
const INF: i32=std::i32::MAX/2;
fn rl() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s
}
fn rv<T>() -> Vec<T> where T: std::str::FromStr, T::Err: std::fmt::Debug, {
    rl().split_whitespace().map(|x|x.parse::<T>().unwrap()).collect()
}