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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include<string>
#include<cmath>
#include<algorithm>
#include<cctype>
#include<queue>
#include<deque>
#include<regex>
#include<stack>
#include<stdio.h>
#include<vector>
#include<set>
#include<map>
#include<iomanip>
#define rep(i,n) for(int i=0;i<n;i++)

typedef int long long ll;
using namespace std;
typedef pair<int,int> P;
int dx[4]={1,0,-1,0};
int dy[4]={0,1,0,-1};
const ll MOD=1e9+7;
static const int MAX = 100;
static const int INF = (1<<23);
template<class T> T gcd(T a, T b){return b? gcd(b,a%b) : a;}
template<class T> T lcm(T a,T b){return a / gcd(a,b)*b;}

int n;
vector<int> v[201];
bool check(int i){

    int col[201];
    rep(j,201)col[j]=-1;
    queue<int> q;
    q.push(i);
    col[i]=0;

    int color = 1;
    while(!q.empty()){
        int sum = q.size();
        rep(j,sum){
            int t = q.front();
            q.pop();
         rep(l,v[t].size()){
             int x = v[t][l];
             if(col[x]==col[t]){
                 return false;
             }else{
                 if(col[x]==-1){
                     q.push(x);
                 }
                 if(col[t]==1){
                     col[x]=0;
                 }else{
                     col[x]=1;
                 }
             }
         }
        }

    }
    return true;




}

int main(){
    cin>>n;
    rep(i,n){
        string s;
        cin>>s;
        rep(j,s.size()){
            if(s[j]=='1'){
                v[i].push_back(j);
            }
        }
    }
    if(!check(0)){
        cout<<-1<<endl;
        return 0;
    }










    
return 0;
}