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: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        var N = sc.ReadInt();
        var S = sc.ReadStrArray(N);
        var G = new List<int>[N];
        for (int i = 0; i < N; i++)
        {
            G[i] = new List<int>();
        }
        var wf = new WarshallFloyd(N);
        for (int i = 0; i < N; i++)
        {
            for (int j = i; j < N; j++)
            {
                if (S[i][j] == '1')
                {
                    G[i].Add(j);
                    G[j].Add(i);
                    wf.SetCost(i, j);
                    wf.SetCost(j, i);
                }
            }
        }
        if (!CheckBipartiteGraph(0, -1, G))
        {
            Console.WriteLine(-1);
            return;
        }
        var dp = wf.CalcMinCost();
        var maxd = 0L;
        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < N; j++)
            {
                maxd = Math.Max(maxd, dp[i, j]);
            }
        }
        var ans = maxd + 1;
        Console.WriteLine(ans);
    }

    class WarshallFloyd
    {
        public int V { get; set; }
        public long[,] DP { get; set; }
        public long INF = long.MaxValue;
        public bool[] Negative;
        public WarshallFloyd(int v)
        {
            this.V = v;
            this.DP = new long[V, V];
            for (int i = 0; i < V; i++)
            {
                for (int j = 0; j < V; j++)
                {
                    this.DP[i, j] = INF;
                }
                this.DP[i, i] = 0;
            }
        }
        public void SetCost(int a, int b, int c = 1)
        {
            this.DP[a, b] = c;
        }
        public long[,] CalcMinCost()
        {
            this.Negative = new bool[V];
            for (int k = 0; k < V; k++)
            {
                for (int i = 0; i < V; i++)
                {
                    for (int j = 0; j < V; j++)
                    {
                        if (DP[i, k] == INF || DP[k, j] == INF) continue;
                        DP[i, j] = Math.Min(DP[i, j], DP[i, k] + DP[k, j]);
                    }
                }
            }
            for (int k = 0; k < V; k++)
            {
                for (int i = 0; i < V; i++)
                {
                    for (int j = 0; j < V; j++)
                    {
                        if (DP[i, k] == INF || DP[k, j] == INF) continue;
                        if (DP[i, j] > DP[i, k] + DP[k, j])
                        {
                            this.Negative[i] = true;
                            this.Negative[j] = true;
                            this.Negative[k] = true;
                        }
                    }
                }
            }
            return DP;
        }
        public long GetMinCost(int a, int b)
        {
            return DP[a, b];
        }
        public bool IsINF(int a, int b)
        {
            return DP[a, b] >= INF;
        }
        public bool IsNegative(params int[] vs)
        {
            if (vs.Length == 0) vs = Enumerable.Range(0, V).ToArray();
            foreach (var v in vs)
            {
                if (Negative[v]) return true;
            }
            return false;
        }
    }

    static int[] Seen;
    static bool CheckBipartiteGraph(int now, int prev, List<int>[] g, int c = 0)
    {
        if (Seen == null) Seen = Enumerable.Repeat(-1, g.Length).ToArray();
        foreach (var next in g[now])
        {
            if (next == prev) continue;
            var nextc = Seen[next];
            if (nextc >= 0 && nextc == c) return false;
            if (nextc >= 0) continue;
            Seen[next] = (c + 1) % 2;
            var res = CheckBipartiteGraph(next, now, g, (c + 1) % 2);
            if (res == false) return false;
        }
        return true;
    }

    static Scanner sc = new Scanner();
}
class Scanner
{
    string[] S = new string[0];
    int Index = 0;
    char[] Separators = new char[] { ' ' };

    public string Next()
    {
        if (this.Index < this.S.Length) return this.S[this.Index++];
        var line = "";
        while (line == "") line = Console.ReadLine();
        this.S = line.Split(this.Separators, StringSplitOptions.RemoveEmptyEntries);
        if (this.S.Length == 0) return this.Next();
        this.Index = 0;
        return this.S[this.Index++];
    }
    public string ReadStr()
    {
        return this.Next();
    }
    public char ReadChar()
    {
        return this.Next()[0];
    }
    public int ReadInt()
    {
        return int.Parse(this.Next());
    }
    public uint ReadUInt()
    {
        return uint.Parse(this.Next());
    }
    public long ReadLong()
    {
        return long.Parse(this.Next());
    }
    public double ReadDouble()
    {
        return double.Parse(this.Next());
    }
    public Tuple<int, int> ReadTup(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add);
    }
    public Tuple<long, long> ReadTupLong(int add = 0)
    {
        return Tuple.Create(this.ReadLong() + add, this.ReadLong() + add);
    }
    public Tuple<int, int, int> ReadTup3(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add);
    }
    public Tuple<int, int, int, int> ReadTup4(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add);
    }
    public int[] ReadIntArray(int n)
    {
        var array = new int[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadInt();
        }
        return array;
    }
    public long[] ReadLongArray(int n)
    {
        var array = new long[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadLong();
        }
        return array;
    }
    public double[] ReadDoubleArray(int n)
    {
        var array = new double[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadDouble();
        }
        return array;
    }
    public char[] ReadCharArray(int n)
    {
        var array = new char[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadChar();
        }
        return array;
    }
    public string[] ReadStrArray(int n)
    {
        var array = new string[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadStr();
        }
        return array;
    }
    public Tuple<long, long>[] ReadTupLongArray(int n, int add = 0)
    {
        var array = new Tuple<long, long>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTupLong(add);
        }
        return array;
    }
    public Tuple<int, int>[] ReadTupArray(int n, int add = 0)
    {
        var array = new Tuple<int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup(add);
        }
        return array;
    }
    public Tuple<int, int, int>[] ReadTup3Array(int n, int add = 0)
    {
        var array = new Tuple<int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup3(add);
        }
        return array;
    }
    public Tuple<int, int, int, int>[] ReadTup4Array(int n, int add = 0)
    {
        var array = new Tuple<int, int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup4(add);
        }
        return array;
    }
}