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: Time Limit Exceeded)

use std::io::{self, BufRead};
use std::collections::BTreeMap;

fn dfs(g: &Vec<Vec<i32>>, path: &mut BTreeMap<usize, usize>, n: usize, p: usize) -> bool {
  if let Some(v) = path.get(&n) {
    let len = path.len() - v;
    return len % 2 == 0;
  }
  let cs: Vec<usize> = g[n].iter().enumerate().filter(|tup| tup.0 != p && *tup.1 == 1).map(|(i, _)| i).collect();
  let size = path.len();
  path.insert(n, size);
  for c in cs {
    if !dfs(g, path, c, n) {
      return false;
    }
  }
  path.remove(&n);
  true
}

fn main() {
  let stdin = io::stdin();
  let mut lines = stdin.lock().lines();
  let n: usize = lines.next().unwrap().unwrap().parse().unwrap();
  let mut g: Vec<Vec<i32>> = Vec::new();
  for _ in 0..n {
    let s = lines.next().unwrap().unwrap().chars().map(|c| if c == '1' { 1 } else { i32::max_value() }).collect();
    g.push(s);
  }
  for i in 0..n {
    g[i][i] = 0;
  }
  let mut path: BTreeMap<usize, usize> = BTreeMap::new();
  if !dfs(&g, &mut path, 0, 0) {
    println!("-1");
    return;
  }
  for k in 0..n {
    for i in 0..n {
      for j in 0..n {
        if g[i][k] != i32::max_value() && g[k][j] != i32::max_value() && g[i][j] > g[i][k] + g[k][j] {
          g[i][j] = g[i][k] + g[k][j];
        }
      }
    }
  }
  let ans = g.iter().map(|l| l.iter().max().unwrap()).max().unwrap();
  println!("{}", ans + 1);
}