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++14 (GCC 5.4.1) (judge verdict: Accepted)

#ifdef LOCAL
    #define _GLIBCXX_DEBUG
    #define __clock__
#else
    #pragma GCC optimize("Ofast")
    // #define NDEBUG
#endif
// #define __buffer_check__
#define __precision__ 10
#define iostream_untie true
#define debug_stream std::cerr

#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <complex>
#include <cstring>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>

#define all(v) std::begin(v), std::end(v)
#define rall(v) std::rbegin(v), std::rend(v)
#define odd(n) ((n) & 1)
#define even(n) (not __odd(n))
#define __popcount(n) __builtin_popcountll(n)
#define __clz32(n) __builtin_clz(n)
#define __clz64(n) __builtin_clzll(n)
#define __ctz32(n) __builtin_ctz(n)
#define __ctz64(n) __builtin_ctzll(n)

using i32 = int_least32_t; using i64 = int_least64_t; using u32 = uint_least32_t; using u64 = uint_least64_t;
using pii = std::pair<i32, i32>; using pll = std::pair<i64, i64>;
template <class T> using heap = std::priority_queue<T>;
template <class T> using rheap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <class T> using hashset = std::unordered_set<T>;
template <class Key, class Value> using hashmap = std::unordered_map<Key, Value>;

namespace setting
{
    using namespace std::chrono;
    system_clock::time_point start_time, end_time;
    long long get_elapsed_time() { end_time = system_clock::now(); return duration_cast<milliseconds>(end_time - start_time).count(); }
    void print_elapsed_time() { debug_stream << "\n----- Exec time : " << get_elapsed_time() << " ms -----\n"; }
    void buffer_check() { char bufc; if(std::cin >> bufc) debug_stream << "\n\033[1;35mwarning\033[0m: buffer not empty.\n"; }
    struct setupper
    {
        setupper()
        {
            if(iostream_untie) std::ios::sync_with_stdio(false), std::cin.tie(nullptr);
            std::cout << std::fixed << std::setprecision(__precision__);
    #ifdef stderr_path
            if(freopen(stderr_path, "a", stderr))
            {
                std::cerr << std::fixed << std::setprecision(__precision__);
            }
    #endif
    #ifdef stdout_path
            if(not freopen(stdout_path, "w", stdout))
            {
                freopen("CON", "w", stdout);
                debug_stream << "\n\033[1;35mwarning\033[0m: failed to open stdout file.\n";
            }
            std::cout << "";
    #endif
    #ifdef stdin_path
            if(not freopen(stdin_path, "r", stdin))
            {
                freopen("CON", "r", stdin);
                debug_stream << "\n\033[1;35mwarning\033[0m: failed to open stdin file.\n";
            }
    #endif
    #ifdef LOCAL
            debug_stream << "\n----- stderr at LOCAL -----\n\n";
            atexit(print_elapsed_time);
    #endif
    #ifdef __buffer_check__
            atexit(buffer_check);
    #endif
    #if defined(__clock__) || defined(LOCAL)
            start_time = system_clock::now();
    #endif
        }
    } __setupper; // struct setupper
} // namespace setting
#ifdef __clock__
class
{
    std::chrono::system_clock::time_point built_pt, last_pt; int built_ln, last_ln;
    std::string built_func, last_func; bool is_built = false;
  public:
    void build(int crt_ln, const std::string &crt_func)
    {
        is_built = true, last_pt = built_pt = std::chrono::system_clock::now(),  last_ln = built_ln = crt_ln, last_func = built_func = crt_func;
    }
    void set(int crt_ln, const std::string &crt_func)
    {
        if(is_built) last_pt = std::chrono::system_clock::now(), last_ln = crt_ln, last_func = crt_func;
        else debug_stream << "[ " << crt_ln << " : " << crt_func << " ] " << "myclock_t::set failed (yet to be built!)\n";
    }
    void get(int crt_ln, const std::string &crt_func)
    {
        if(is_built)
        {
            std::chrono::system_clock::time_point crt_pt(std::chrono::system_clock::now());
            long long diff = std::chrono::duration_cast<std::chrono::milliseconds>(crt_pt - last_pt).count();
            debug_stream << diff << " ms elapsed from" << " [ " << last_ln << " : " << last_func << " ]";
            if(last_ln == built_ln) debug_stream << " (when built)";
            debug_stream << " to" << " [ " << crt_ln << " : " << crt_func << " ]" << "\n";
            last_pt = built_pt, last_ln = built_ln, last_func = built_func;
        }
        else
        {
            debug_stream << "[ " << crt_ln << " : " << crt_func << " ] " << "myclock_t::get failed (yet to be built!)\n";
        }
    }
} myclock; // unnamed class
    #define build_clock() myclock.build(__LINE__, __func__)
    #define set_clock() myclock.set(__LINE__, __func__)
    #define get_clock() myclock.get(__LINE__, __func__)
#else
    #define build_clock() ((void)0)
    #define set_clock() ((void)0)
    #define get_clock() ((void)0)
#endif

namespace std
{
    // hash
    template <class T> size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash<T>()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); }
    template <class T, class U> struct hash<pair<T, U>> { size_t operator()(pair<T, U> const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } };
    template <class tuple_t, size_t index = tuple_size<tuple_t>::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc<tuple_t, index - 1>::apply(seed, t), get<index>(t)); } };
    template <class tuple_t> struct tuple_hash_calc<tuple_t, 0> { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } };
    template <class... T> struct hash<tuple<T...>> { size_t operator()(tuple<T...> const &t) const { return tuple_hash_calc<tuple<T...>>::apply(0, t); } };
    // iostream
    template <class T, class U> istream &operator>>(istream &is, pair<T, U> &p) { return is >> p.first >> p.second; }
    template <class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { return os << p.first << ' ' << p.second; }
    template <class tuple_t, size_t index> struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis<tuple_t, index - 1>::apply(is, t); return is >> get<index>(t); } };
    template <class tuple_t> struct tupleis<tuple_t, SIZE_MAX> { static istream &apply(istream &is, tuple_t &t) { return is; } };
    template <class... T> istream &operator>>(istream &is, tuple<T...> &t)  { return tupleis<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(is, t); }
    template <> istream &operator>>(istream &is, tuple<> &t) { return is; }
    template <class tuple_t, size_t index> struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos<tuple_t, index - 1>::apply(os, t); return os << ' ' << get<index>(t); } };
    template <class tuple_t> struct tupleos<tuple_t, 0> { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } };
    template <class... T> ostream &operator<<(ostream &os, const tuple<T...> &t)  { return tupleos<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(os, t); }
    template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; }
    template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
    istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; }
    template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
    ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; }
} // namespace std

#ifdef LOCAL
    #define dump(...)                                                              \
        debug_stream << "[ " << __LINE__ << " : " << __FUNCTION__ << " ]\n",       \
            dump_func(#__VA_ARGS__, __VA_ARGS__)
    template <class T> void dump_func(const char *ptr, const T &x)
    {
        debug_stream << '\t';
        for(char c = *ptr; c != '\0'; c = *++ptr) if(c != ' ') debug_stream << c;
        debug_stream << " : " << x << '\n';
    }
    template <class T, class... rest_t> void dump_func(const char *ptr, const T &x, rest_t... rest)
    {
        debug_stream << '\t';
        for(char c = *ptr; c != ','; c = *++ptr) if(c != ' ') debug_stream << c;
        debug_stream << " : " << x << ",\n"; dump_func(++ptr, rest...);
    }
#else
    #define dump(...) ((void)0)
#endif

template <class T = int> T read() { T x; std::cin >> x; return x; }
template <class iterator> void read(iterator __first, iterator __last) { for(iterator i = __first; i != __last; ++i) std::cin >> *i; }
template <class iterator> void write(iterator __first, iterator __last) { for(iterator i = __first; i != __last; std::cout << (++i == __last ? "" : " ")) std::cout << *i; }

// substitute y for x if x > y.
template <class T> inline bool sbmin(T &x, const T &y) { return x > y ? x = y, true : false; }
// substitute y for x if x < y.
template <class T> inline bool sbmax(T &x, const T &y) { return x < y ? x = y, true : false; }

// binary search on integers.
long long bin(long long __ok, long long __ng, const std::function<bool(long long)> &pred)
{
    while(std::abs(__ok - __ng) > 1)
    {
        long long mid{(__ok + __ng) >> 1};
        (pred(mid) ? __ok : __ng) = mid;
    }
    return __ok;
}
// binary search on real numbers.
long double bin(long double __ok, long double __ng, const long double eps, const std::function<bool(long double)> &pred)
{
    while(std::abs(__ok - __ng) > eps)
    {
        long double mid{(__ok + __ng) / 2};
        (pred(mid) ? __ok : __ng) = mid;
    }
    return __ok;
}
// binary search on integers(with a class member function).
template <class X, class int_t1, class int_t2, class int_t3>
int_t1 bin(int_t2 __ok, int_t3 __ng, bool (X::*const pred)(int_t1), X *const x)
{
    int_t1 ok(__ok), ng(__ng);
    while(std::abs(ok - ng) > 1)
    {
        int_t1 mid{(ok + ng) >> 1};
        ((x->*pred)(mid) ? ok : ng) = mid;
    }
    return ok;
}
// binary search on real numbers(with a class member function).
template <class X, class real_t1, class real_t2, class real_t3, class real_t4>
real_t1 bin(real_t2 __ok, real_t3 __ng, const real_t4 eps, bool (X::*const pred)(real_t1), X *const x)
{
    real_t1 ok(__ok), ng(__ng);
    while(std::abs(ok - ng) > eps)
    {
        real_t1 mid{(ok + ng) / 2};
        ((x->*pred)(mid) ? ok : ng) = mid;
    }
    return ok;
}

// be careful that val is type-sensitive.
template <class T, class A, size_t N> void init(A (&array)[N], const T &val) { std::fill((T*)array, (T*)(array + N), val); }

// reset all bits.
template <class A> void reset(A &array) { memset(array, 0, sizeof(array)); }


/* The main code follows. */

using namespace std;

class union_find
{
    std::vector<int> dat;
    bool *const cyc, *const clr, *const flip;
    size_t comp, isol;
    bool bipart;

  public:
    explicit union_find(const int n) : dat(n, -1), cyc(new bool[n]{}), clr(new bool[n]{}), flip(new bool[n]{}), comp(n), isol(n), bipart(true) {}
    ~union_find() { delete[] cyc; delete[] clr; delete[] flip; }

    int find(const int x)
    {
        assert(x < size());
        if(dat[x] < 0) return x;
        const int r = find(dat[x]);
        if(flip[dat[x]])
        {
            clr[x] = !clr[x];
            flip[x] = !flip[x];
        }
        return dat[x] = r;
    }

    size_t size() const { return dat.size(); }
    size_t size(const int x) { return -dat[find(x)]; }

    size_t count() const { return comp; }

    size_t isolated() const { return isol; }

    bool color(const int x) { return find(x), clr[x]; }

    bool cyclic(const int x) { return cyc[find(x)]; }

    bool same(const int x, const int y) { return find(x) == find(y); }

    bool bipartite() const { return bipart; }

    bool unite(int x, int y)
    {
        const int _x = find(x);
        const int _y = find(y);
        const bool f = clr[x] == clr[y];
        x = _x, y = _y;
        if(x == y)
        {
            bipart &= !f;
            cyc[x] = true;
            return false;
        }
        if(dat[x] > dat[y]) std::swap(x, y);
        if(dat[x] == -1) --isol;
        if(dat[y] == -1) --isol;
        dat[x] += dat[y];
        dat[y] = x;
        cyc[x] = cyc[x] || cyc[y];
        if(f)
        {
            clr[y] = !clr[y];
            flip[y] = !flip[y];
        }
        --comp;
        return true;
    }
}; // class union_find


int main(int argc, char *argv[])
{
    int n;
    cin >> n;
    vector<string> g(n);
    cin >> g;
    int dist[222][222];
    init(dist, n);
    union_find uf(n);
    for(int i = 0; i < n; ++i)
    {
        for(int j = 0; j < n; ++j)
        {
            if(g[i][j] - '0')
            {
                uf.unite(i,j);
                dist[i][j] = 1;
            }
            else
            {
                if(i==j)
                {
                    dist[i][j]=0;
                }
            }
        }
    }
    for(int k = 0; k < n; ++k)
    {
        for(int i = 0; i < n; ++i)
        {
            for(int j = 0; j < n; ++j)
            {
                sbmin(dist[i][j], dist[i][k] + dist[k][j]);
            }
        }
    }

    if(uf.bipartite())
    {
        int ans=0;
        for(int i = 0; i < n; ++i)
        {
            vector<int> comp;
            for(int j = 0; j < n; ++j)
            {
                if(uf.find(j)==i)
                {
                    comp.emplace_back(j);
                }
            }
            int k=0;
            for(int a : comp)
            {
                for(int b : comp)
                {
                    sbmax(k,dist[a][b]+1);
                }
            }
            ans+=k;
        }
        cout << ans << "\n";
    }
    else
    {
        cout << -1 << "\n";
    }
}