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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.InteropServices;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using static Math2;
using static io;
using static Utils;

public class CP {
  public void Solve() {
    var N = Int1;
    var S = Enumerable.Range(0, N).Select(_ => Chars.Select(x => (long) (x - '0')).ToArray()).ToArray();

    if (!Graph.IsBipartiteGraph(Graph.toli(S))) {
      Put(-1);
      return;
    }
    var ans = 0L;
    var dists = Graph.Warshall_Floyd(Graph.toli(S));
    foreach (var x in dists) {
      foreach (var item in x) {
        ans = Max(ans, item);
      }
    }
    Put(ans + 1);
  }

}

public static class Graph {
  public static long[] dijkstra(List<Tuple<long, int>>[] edge, int from, long INF = Math2.INFL) {
    long[] ret = Enumerable.Range(0, edge.Length).Select(_ => INF).ToArray();
    var pq = new PriorityQueue<Tuple<long, int>>((a, b) => (int) (a.Item1 - b.Item1));
    ret[from] = 0;
    pq.Enqueue(new Tuple<long, int>(0, from));
    while (pq.Count > 0) {
      var p = pq.Dequeue();
      var v = p.Item2;
      if (ret[v] < p.Item1) continue;
      foreach (var e in edge[v]) {
        if (ret[e.Item2] > ret[v] + e.Item1) {
          ret[e.Item2] = ret[v] + e.Item1;
          pq.Enqueue(new Tuple<long, int>(ret[e.Item2], e.Item2));
        }

      }
    }
    return ret;
  }
  public static long[][] Warshall_Floyd(List<Tuple<long, int>>[] edge) {
    var ret = new long[edge.Length][];
    for (int i = 0; i < edge.Length; ++i) {
      ret[i] = Enumerable.Repeat(INFL, edge.Length).ToArray();
    }
    for (int i = 0; i < edge.Length; ++i) {
      foreach (var x in edge[i]) {
        ret[i][x.Item2] = x.Item1;
      }
    }
    for (int k = 0; k < edge.Length; ++k) {
      for (int i = 0; i < edge.Length; ++i) {
        for (int j = 0; j < edge.Length; ++j) {
          ret[i][j] = Min(ret[i][j], ret[i][k] + ret[k][j]);
        }
      }
    }
    return ret;

  }
  public static bool IsBipartiteGraph(List<Tuple<long, int>>[] edge) {
    var color = Enumerable.Repeat(-1, edge.Length).ToArray();
    Func<int, int, bool> dfs = null;
    dfs = (int v, int c) => {
      color[v] = c;
      foreach (var nv in edge[v]) {
        if (color[nv.Item2] == c) return false;
        if (color[nv.Item2] == -1 && !dfs(nv.Item2, 1 - c)) return false;
      }
      return true;
    };
    for (int i = 0; i < edge.Length; ++i) {
      if (color[i] == -1) {
        if (!dfs(i, 0)) {
          return false;
        }
      }
    }
    return true;
  }
  public static List<Tuple<long, int>>[] totp(List<int>[] lis) {
    var ret = new List<Tuple<long, int>>[lis.Length];
    for (int i = 0; i < lis.Length; ++i) {
      ret[i] = new List<Tuple<long, int>>();
      foreach (var x in lis[i]) {
        ret[i].Add(new Tuple<long, int>(1, x));
      }
    }
    return ret;
  }
  public static long[][] tomat(List<Tuple<long, int>>[] edge) {
    var ret = new long[edge.Length][];
    for (int i = 0; i < edge.Length; ++i) {
      ret[i] = new long[edge.Length];
      for (int j = 0; j < edge.Length; ++j) {
        ret[i][j] = Math2.INFL;
      }
    }
    for (int i = 0; i < edge.Length; ++i) {
      foreach (var x in edge[i]) {
        ret[i][x.Item1] = x.Item2;
      }
    }
    return ret;
  }
  public static List<Tuple<long, int>>[] toli(long[][] s) {
    var ret = new List<Tuple<long, int>>[s.Length];
    for (int i = 0; i < s.Length; ++i) ret[i] = new List<Tuple<long, int>>();
    for (int i = 0; i < s.Length; ++i) {
      for (int j = 0; j < s.Length; ++j) {
        if (s[i][j] != 0) ret[i].Add(new Tuple<long, int>(s[i][j], j));
      }
    }
    return ret;
  }

}

public class BinarySearch {
  public static int Lower_Bound<T>(IList<T> Array, T Target) {
    return Lower_Bound<T>(Array, Target, Comparer<T>.Default.Compare);
  }
  public static int Lower_Bound<T>(IList<T> Array, T Target, Comparison<T> Comp) {
    var cmp = Comparer<T>.Create(Comp);
    var l = -1; //always ng
    var r = Array.Count(); //always ok
    while (r - l > 1) {
      var mid = l + (r - l) / 2;
      var res = cmp.Compare(Array[mid], Target);
      if (res >= 0) r = mid;
      else l = mid;
    }
    return r;
  }
  public static int Upper_Bound<T>(IList<T> Array, T Target) {
    return Upper_Bound<T>(Array, Target, Comparer<T>.Default.Compare);
  }
  public static int Upper_Bound<T>(IList<T> Array, T Target, Comparison<T> Comp) {
    var cmp = Comparer<T>.Create(Comp);
    var l = -1;
    var r = Array.Count;
    while (r - l > 1) {
      var mid = l + (r - l) / 2;
      var res = cmp.Compare(Array[mid], Target);
      if (res > 0) r = mid;
      else l = mid;
    }
    return r;
  }
}
public static class Math2 {
  public const int INF = 1 << 29;
  public const long INFL = 1L << 60;
  public const long MOD = 1000000007;
  public const int MOD2 = 998244353;

  public static long Power(long a, long b, long MOD = 1000000007) //i^N
  {
    long res = 1;
    while (b > 0) {
      if ((b & 1) != 0) res = res * a % MOD;
      a = a * a % MOD;
      b >>= 1;
    }
    return res;
  }
  public static long Power2(long a, long b) //i^N
  {
    long res = 1;
    while (b > 0) {
      if ((b & 1) != 0) res = res * a;
      a = a * a;
      b >>= 1;
    }
    return res;
  }
  public static long GCD(long a, long b) {
    while (b > 0) {
      var r = a % b;
      a = b;
      b = r;
    }
    return a;
  }
  public static long LCM(long a, long b) => (b / GCD(a, b)) * a;
  public static long Comb(long n, long r, int MOD = 1000000007) {
    if (r > n - r) r = n - r;
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i) {
      Deno = (Deno * i) % MOD;
      Nume = Nume * (n - i + 1) % MOD;
    }
    return (Nume * inv(Deno)) % MOD;
  }
  public static long Comb2(long n, long r) {
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i) {
      Deno *= i;
      Nume *= n - i + 1;
    }
    return Nume / Deno;
  }
  public static long inv(long x, int MOD = 1000000007) {
    return Power(x, MOD - 2, MOD);
  }
}
public static class Utils {
  public static void Swap<T>(ref T A, ref T B) {
    T x = A;
    A = B;
    B = x;
  }
  public static int DigitSum(int N) {
    string s = N.ToString();
    int ret = 0;
    for (int i = 0; i < s.Length; ++i) ret += s[i] - '0';
    return ret;
  }
  public static string ConvertBase(long N, int K) {
    StringBuilder ret = new StringBuilder();
    while (N > 0) {
      var r = N % K;
      N /= K;
      ret.Append(r);
    }
    return new string(ret.ToString().ToCharArray().Reverse().ToArray());
  }
}
public class PriorityQueue<T> {
  List<T> _item;
  public int Count { get { return _item.Count; } }
  bool _isascend { get; set; }
  public T Peek { get { return _item[0]; } }
  Comparison<T> Comp;
  public PriorityQueue(bool IsAscend = true, IEnumerable<T> list = null) : this(Comparer<T>.Default.Compare, IsAscend, list) { }
  public PriorityQueue(Comparison<T> cmp, bool IsAscend = true, IEnumerable<T> list = null) {
    _item = new List<T>();
    _isascend = IsAscend;
    this.Comp = cmp;
    if (list != null) {
      _item.AddRange(list);
      Build();
    }
  }

  private int Compare(int i, int j) => (_isascend ? -1 : 1) * Comp(_item[i], _item[j]);
  private void Swap(int i, int j) { var t = _item[i]; _item[i] = _item[j]; _item[j] = t; }
  private int Parent(int i) => (i - 1) >> 1;
  private int Left(int i) => (i << 1) + 1;
  public T Enqueue(T val) {
    int i = _item.Count;
    _item.Add(val);
    while (i > 0) {
      int p = Parent(i);
      if (Compare(i, p) > 0)
        Swap(i, p);
      i = p;
    }
    return val;
  }
  private void Heapify(int index) {
    for (int i = index, j;
      (j = Left(i)) < _item.Count; i = j) {
      if (j != _item.Count - 1 && Compare(j, j + 1) < 0) j++;
      if (Compare(i, j) < 0)
        Swap(i, j);
    }
  }
  public T Dequeue() {
    T val = _item[0];
    _item[0] = _item[_item.Count - 1];
    _item.RemoveAt(_item.Count - 1);
    Heapify(0);
    return val;
  }
  private void Build() {
    for (var i = (_item.Count >> 1) - 1; i >= 0; i--)
      Heapify(i);
  }
}
class Program {
  static void Main(string[] args) {
    var CP = new CP();
    CP.Solve();
  }
}
public static class io {
  public static string Str => Console.ReadLine();
  public static string[] Strs => Str.Split(' ');
  public static long[] Longs => Strs.Select(long.Parse).ToArray();
  public static int[] Ints => Strs.Select(int.Parse).ToArray();
  public static char[] Chars => Str.ToArray();
  public static double[] Doubles => Strs.Select(double.Parse).ToArray();
  public static long Long1 => Longs[0];
  public static int Int1 => Ints[0];
  public static char Char1 => Chars[0];
  public static double Double1 => Doubles[0];
  public static long[] VerticalRead(int N) { long[] A = new long[N]; for (int i = 0; i < N; ++i) A[i] = Long1; return A; }
  public static void Put(string a) => Console.WriteLine(a);
  public static void Put(params object[] i) => Put(string.Join(" ", i));
  public static void Put<T>(IEnumerable<T> a) => Put(string.Join(" ", a));
  public static void VerticalPut<T>(IEnumerable<T> a) { foreach (var z in a) Put(z); }
  public static void YN(bool i) {
    if (i) Put("Yes");
    else Put("No");
  }
}