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(non_snake_case)]
#![allow(unused_variables)]
#![allow(dead_code)]

fn main() {
    let N: usize = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.trim().parse().unwrap()
    };
    let S: Vec<Vec<char>> = (0..N).map(|_| {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.trim().chars().collect()
    }).collect();

    // グラフが二部グラフならば真を返す
    fn f(i: usize, c: i64, cs: &mut Vec<i64>, N: usize, S: &Vec<Vec<char>>) -> bool {
        if cs[i] != 0 {
            c == cs[i]
        } else {
            cs[i] = c;
            (0..N).all(|j| S[i][j] == '0' || f(j, -c, cs, N, S))
        }
    }
    let mut cs = vec![0; N];
    let ans = if f(0, 1, &mut cs, N, &S) {
        const INF: i64 = 1_000_000_000;
        let mut dp = vec![vec![INF; N]; N];
        for i in 0..N { dp[i][i] = 0; }
        for i in 0..N { for j in 0..N { if S[i][j] == '1' { dp[i][j] = 1; } } }
        for k in 0..N { for i in 0..N { for j in 0..N { dp[i][j] = std::cmp::min(dp[i][j], dp[i][k] + dp[k][j]); } } }
        1 + (0..N).map(|i| *dp[i].iter().max().unwrap()).max().unwrap()
    } else {
        -1
    };

    println!("{}", ans);
}