Problem:
Score : 400 points

Problem Statement

Takahashi has a maze, which is a grid of H \times W squares with H horizontal rows and W vertical columns.

The square at the i-th row from the top and the j-th column is a "wall" square if S_{ij} is #, and a "road" square if S_{ij} is ..

From a road square, you can move to a horizontally or vertically adjacent road square.

You cannot move out of the maze, move to a wall square, or move diagonally.

Takahashi will choose a starting square and a goal square, which can be any road squares, and give the maze to Aoki.

Aoki will then travel from the starting square to the goal square, in the minimum number of moves required.

In this situation, find the maximum possible number of moves Aoki has to make.

Constraints

1 \leq H,W \leq 20

S_{ij} is . or #.

S contains at least two occurrences of ..

Any road square can be reached from any road square in zero or more moves.

Input

Input is given from Standard Input in the following format:

H W
S_{11}...S_{1W}
:
S_{H1}...S_{HW}

Output

Print the maximum possible number of moves Aoki has to make.

Sample Input 1

3 3
...
...
...

Sample Output 1

4

If Takahashi chooses the top-left square as the starting square and the bottom-right square as the goal square, Aoki has to make four moves.

Sample Input 2

3 5
...#.
.#.#.
.#...

Sample Output 2

10

If Takahashi chooses the bottom-left square as the starting square and the top-right square as the goal square, Aoki has to make ten moves.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include "bits/stdc++.h"
#pragma GCC optimize("Ofast")

// Begin Header {{{
using namespace std;

#ifndef DEBUG
#define dump(...)
#endif

#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define rep(i, n) for (intmax_t i = 0, i##_limit = (n); i < i##_limit; ++i)
#define reps(i, b, e) for (intmax_t i = (b), i##_limit = (e); i <= i##_limit; ++i)
#define repr(i, b, e) for (intmax_t i = (b), i##_limit = (e); i >= i##_limit; --i)
#define var(Type, ...) Type __VA_ARGS__; input(__VA_ARGS__)

constexpr size_t    operator""_zu(unsigned long long value) { return value; };
constexpr intmax_t  operator""_jd(unsigned long long value) { return value; };
constexpr uintmax_t operator""_ju(unsigned long long value) { return value; };

constexpr int INF = 0x3f3f3f3f;
constexpr intmax_t LINF = 0x3f3f3f3f3f3f3f3f_jd;

namespace moke {

template <class T> using MaxHeap = priority_queue<T, vector<T>, less<T>>;
template <class T> using MinHeap = priority_queue<T, vector<T>, greater<T>>;

inline void input() {}
template <class Head, class... Tail> inline void input(Head&& head, Tail&&... tail) {
    cin >> head;
    input(forward<Tail>(tail)...);
}

inline void outs() { cout << "\n"; }
template <class Head, class... Tail> inline void outs(Head&& head, Tail&&... tail) {
    cout << head << (sizeof...(tail) ? " " : "");
    outs(forward<Tail>(tail)...);
}

template <class T> inline void outs(vector<T> &vec) {
    for (auto &e : vec) cout << e << " \n"[&e == &vec.back()];
}

template <class T> inline void outs(vector<vector<T>> &df) {
    for (auto &vec : df) outs(vec);
}

inline void outl() { cout << "\n"; }
template <class Head, class... Tail> inline void outl(Head&& head, Tail&&... tail) {
    cout << head << (sizeof...(tail) ? "\n" : "");
    outl(forward<Tail>(tail)...);
}

template <class T> inline void outl(vector<T> &vec) {
    for (auto &e : vec) cout << e << "\n";
}

inline void outn() {}
template <class Head, class... Tail> inline void outn(Head&& head, Tail&&... tail) {
    cout << head;
    outn(forward<Tail>(tail)...);
}

template <class T> inline void outn(vector<T> &vec) {
    for (auto &e : vec) cout << e;
}

template <class T> inline vector<T> make_v(const T &initValue, size_t sz) {
    return vector<T>(sz, initValue);
}

template <class T, class... Args> inline auto make_v(const T &initValue, size_t sz, Args... args) {
    return vector<decltype(make_v<T>(initValue, args...))>(sz, make_v<T>(initValue, args...));
}

template <class A, class B> inline bool chmax(A &a, const B &b) noexcept {
    return b > a && (a = b, true);
}

template <class A, class B> inline bool chmin(A &a, const B &b) noexcept {
    return b < a && (a = b, true);
}

template <class A, class B> inline common_type_t<A, B> min(const A &a, const B &b) noexcept {
    return a < b ? a : b;
}

template <class A, class B, class... Args>
inline common_type_t<A, B, Args...> min(const A &a, const B &b, const Args&... args) noexcept {
    return moke::min(a < b ? a : b, args...);
}

template <class A, class B> inline common_type_t<A, B> max(const A &a, const B &b) noexcept {
    return a > b ? a : b;
}

template <class A, class B, class... Args>
inline common_type_t<A, B, Args...> max(const A &a, const B &b, const Args&... args) noexcept {
    return moke::max(a > b ? a : b, args...);
}

template <class A, class B> inline common_type_t<A, B> diff(const A &a, const B &b) noexcept {
    return a < b ? b - a : a - b;
}

} // namespace moke

// }}} End Header

namespace moke {

constexpr int dy[] = {0, 1, 0, -1, -1, 1, 1, -1};
constexpr int dx[] = {1, 0, -1, 0, 1, 1, -1, -1};

inline bool inside(int y, int x, int H, int W) {
    return (y >= 0 && x >= 0 && y < H && x < W);
}

int main_() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    var(int, H, W);

    vector<string> mat(H);
    for (auto &s: mat) input(s);

    intmax_t maxv = 0;
    rep(sy, H) rep(sx, W) {
        if (mat[sy][sx] == '.') {
            queue<pair<int, int>> que;
            que.emplace(sy, sx);

            auto dist = make_v<int>(INF, H, W);
            dist[sy][sx] = 0;

            while (!que.empty()) {
                int y, x;
                tie(y, x) = que.front();
                que.pop();
                rep(i, 4) {
                    int ny = y + dy[i];
                    int nx = x + dx[i];
                    if (inside(ny, nx, H, W) && chmin(dist[ny][nx], dist[y][x] + 1) && mat[ny][nx] != '#') {
                        que.emplace(ny, nx);
                    }
                }
            }

            intmax_t valid = 0;
            rep(y, H) rep(x, W) {
                if (dist[y][x] != INF) {
                    chmax(valid, dist[y][x]);
                }
            }

            chmax(maxv, valid);
        }
    }

    outl(maxv);

    return 0;
}

} // namespace moke

signed main() { // {{{
    moke::main_();
    return 0;
} // }}}