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 (1.42.0) (judge verdict: Accepted)

use proconio::input;

#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars, Usize1};
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::ops::*;
#[derive(Clone, Debug, Default)]
struct Struct;

// 最も遠い点までの距離を計算
// 二部グラフになるはず
fn calc_dist(start: usize, n: usize, s: &Vec<Vec<char>>) -> Option<usize> {
    let mut q = VecDeque::new();
    let mut dist = vec![None; n];
    q.push_back((start, 1));

    let mut max_dist = 0;
    while let Some((i, d)) = q.pop_front() {
        if let Some(old_d) = dist[i] {
            if d != old_d {
                return None;
            }
        } else {
            dist[i] = Some(d);
            max_dist = max(max_dist, d);
            for j in 0..n {
                if s[i][j] == '1' && dist[j] != Some(d - 1) {
                    q.push_back((j, d + 1));
                }
            }
        }
    }
    return Some(max_dist);
}

//#[proconio::fastout]
fn main() {
    input! {
        n: usize,
        s:[Chars;n],
    }

    let mut v = Vec::new();
    for i in 0..n {
        if let Some(d) = calc_dist(i, n, &s) {
            v.push(d);
        }
    }
    if let Some(d) = v.iter().max() {
        println!("{}", d);
    } else {
        println!("-1");
    }
}