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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <string>
#include <deque>
#include <numeric>
#include <set>
using namespace std;

const int INF = 1e+9;

int n;
vector<int> graph[205];
int color[205];
bool bipartite_jugding(int v, int c){
    if(color[v] != 0)   return color[v] * c > 0;

    color[v] = c;
    bool res = true;
    for(int i = 0; i < (int)graph[v].size(); ++i){
        res &= bipartite_jugding(graph[v][i], -c);
    }

    return res;
}

int dist[205][205];
void warshall_floyd(){
    for(int k = 0; k < n; ++k){
        for(int i = 0; i < n; ++i){
            for(int j = 0; j < n; ++j){
                dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
            }
        }
    }
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    cin >> n;
    fill((int*)dist, (int*)(dist + n), INF);
    for(int i = 0; i < n; ++i){
        string s;
        cin >> s;
        for(int j = 0; j < n; ++j){
            if(i < j && s[j] == '1'){
                graph[i].push_back(j);
                graph[j].push_back(i);
                dist[i][j] = 1;
                dist[j][i] = 1;
            }
        }
    }
    for(int i = 0; i < n; ++i){
        dist[i][i] = 0;
    }

    if(!bipartite_jugding(0, 1)){
        cout << -1 << endl;
        return 0;
    }

    int res = 0;
    warshall_floyd();
    for(int i = 0; i < n; ++i){
        for(int j = 0; j < n; ++j){
            if(dist[i][j] != INF){
                res = max(res, dist[i][j]);
            }
        }
    }

    cout << res + 1 << endl;
}