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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static List<int>[] li;
	static bool[] b;
	static int[] h;
	static void Main(){
		Sc sc=new Sc();
		int[] s=sc.Ia;
		int n=s[0];
		li=new List<int>[n+1];
		b=new bool[n+1];
		h=new int[n+1];
		for(int i=1;i<=n;i++){li[i]=new List<int>();}
		for(int i=1;i<=n;i++){
			var e=sc.S;
			for(int j =	i;j<e.Length;j++) {
				if(e[j]=='1'){
					li[i].Add(j+1);
					li[j+1].Add(i);
				}
			}
		}
		var qu=new Queue<Tuple<int,int>>();
		qu.Enqueue(Tuple.Create(1,1));
		int c=0;
		bool bo=true;
		while(qu.Count>0){
			var e=qu.Dequeue();
			if(b[e.Item1]){
				if(h[e.Item1]%2!=e.Item2%2){bo=false;}
				continue;
			}
			b[e.Item1]=true;
			h[e.Item1]=e.Item2;
			c=e.Item1;
			for(int i = 0;i<li[e.Item1].Count;i++) {
				if(!b[li[e.Item1][i]]){
					qu.Enqueue(Tuple.Create(li[e.Item1][i],e.Item2+1));
				}
				else if(h[e.Item1]%2==h[li[e.Item1][i]]%2){bo=false;}
			}
		}
		if(!bo){Console.WriteLine("{0}",-1);return;}
		b=new bool[n+1];
		qu=new Queue<Tuple<int,int>>();
		qu.Enqueue(Tuple.Create(c,1));
		while(qu.Count>0){
			var e=qu.Dequeue();
			if(b[e.Item1]){continue;}
			b[e.Item1]=true;
			c=e.Item2;
			for(int i = 0;i<li[e.Item1].Count;i++) {
				if(!b[li[e.Item1][i]]){
					qu.Enqueue(Tuple.Create(li[e.Item1][i],e.Item2+1));
				}
			}
		}
		Console.WriteLine("{0}",c);
	}
	static void Fu(int a,int g){
		b[a]=true;
		h[a]=g;
		for(int i=0;i<li[a].Count;i++){
			if(!b[li[a][i]]){Fu(li[a][i],g);}
		}
	}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}