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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

# coding: utf-8
import sys
#from operator import itemgetter
sysread = sys.stdin.buffer.readline
read = sys.stdin.buffer.read
#from heapq import heappop, heappush
#from collections import defaultdict
sys.setrecursionlimit(10**7)
#import math
#from itertools import product, accumulate, combinations, product
#import bisect
#import numpy as np
#from copy import deepcopy
from collections import deque
#from decimal import Decimal
#from numba import jit

INF = 1 << 50

def bfs(MAZE, goal, start, seen, H, W):
    queue = deque([start + (0 ,)])
    while queue:
        y,x,count = queue.popleft()
        if (y, x) == goal:
            return count
        for i,j in ((0,1), (0,-1), (1,0), (-1, 0)):
            next_y, next_x = y + i, x + j
            if 1 <= next_x <= W and 1 <= next_y <= H and not seen[next_y][next_x] and MAZE[next_y][next_x] == '.':
                seen[next_y][next_x] = 1
                queue.append((next_y, next_x, count+1))
    return False


def dfs(MAZE, goal, current, seen, H, W, min_count = INF):
    y, x, count = current
    #print(x,y,count)
    if count > min_count:
        return min_count
    if (y,x) == goal:
        min_count = min(min_count, count)
    else:
        for i,j in ((0,1), (0,-1), (1,0), (-1, 0)):
            next_y, next_x = y+i, x+j
            if not seen[next_y][next_x] and MAZE[next_y][next_x] == '.':
                seen[next_y][next_x] = 1
                min_count = min(dfs(MAZE, goal, (next_y, next_x, count+1), seen, H, W, min_count), min_count)
                seen[next_y][next_x] = 0
    return min_count

def run():
    H, W = map(int, input().split())
    MAZE = ['#' * (W+2)]
    for _ in range(H):
        s = input()
        s = '#' + s + '#'
        MAZE.append(s)
    MAZE.append('#' * (W+2))

    ways = []
    for i in range(1, H+1):
        for j in range(1, W+1):
            if MAZE[i][j] == '.':ways.append((i, j))

    max_count = 0
    for s_i, s_j in ways:
        for g_i, g_j in ways:
            if s_i == g_i and s_j == g_j:continue
            seen = [[0] * (W+2) for i in range(H+1)]
            min_count = bfs(MAZE, (g_i, g_j), (s_i, s_j), seen, H, W)
            #print((s_i, s_j), '->', (g_i, g_j))
            #print(min_count)
            if not min_count:
                continue
            max_count = max(max_count, min_count)

    print(max_count)

if __name__ == "__main__":
    run()