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 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
int MIN(int a,int b){return a<b?a:b;}   
int main(){
  int n,i,j,k,max=0,d[210][210]={};
  scanf("%d",&n);
  for(i=0;i<n;i++){
    for(j=0;j<n;j++)scanf("%1d",&d[i][j]);
  }
  for(i=0;i<n;i++){
    for(j=0;j<n;j++){
      if(i==j)d[i][j]=0;
      else if(d[i][j]==0)d[i][j]=1e9;
    }
  }
  for(i=0;i<n;i++){
    for(j=0;j<n;j++){
      for(k=0;k<n;k++)d[j][k]=MIN(d[j][k],d[j][i]+d[i][k]);
    }
  }
  for(i=0;i<n;i++){
    k=(d[0][0]+d[i][0])%2;
    for(j=0;j<n;j++){
      if((d[0][j]+d[i][j])%2-k)goto END;
      if(max<d[i][j])max=d[i][j];
    }
  }
  printf("%d\n",max+1);
  return 0;
 END:;
  printf("-1\n");
  return 0;
}