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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

Main(myin());
function myin(){return require("fs").readFileSync("/dev/stdin", "utf8").trim();}
function myout(t){console.log(t);}//standard output
function myerr(t){console.error(t);}//standard error
//[no]param
//不明値:何もしない  1:数値へ変換  2:半角SPで分割  3:改行で分割  4:半角SPで分割し、数値配列へ
//5:改行で分割し、数値配列へ  6:1文字に分割  7:1文字に分割し、数値配列へ
//8:半角SPで結合　9:改行で結合　0:文字なしで結合
function myconv(i,no){switch(no){case 1:return parseInt(i);case 2:return i.split(" ");case 3:return i.split("\n");case 4:return i.split(" ").map((a)=>Number(a));case 5:return i.split("\n").map((a)=>Number(a));case 6:return i.split("");case 7:return i.split("").map((a)=>Number(a));case 8:return i.join(" ");case 9:return i.join("\n");case 0:return i.join("");default:return i;}}
function Main(input) {
  input = myconv(input,3);
  var H = myconv(input[0],4)[0];
  var W = myconv(input[0],4)[1];
  input.shift();
  var output = 0;
  for(var i = 0; i < H; i++){
    for(var j = 0; j < W; j++){
      var tmp = myconv(input[i],6);
      if(tmp[j] == "."){
         for(var k = 0; k < H; k++){
           for(var l = 0; l < W; l++){
             var tmp2 = myconv(input[k],6);
             if(i == k && j == l){
                continue;
             }
             if(tmp2[l] == "."){
                //ここでij地をスタート、kl地をゴールとしてtestに放り込む。
               //その時の距離をoutputに投げる
               //myout(test(i+1,j+1,k+1,l+1));
               output = Math.max(output,test(i,j,k,l));
             }
           }
         }
      }
    }
  }
  //test(1,1,3,4)
  myout(output);
  
  function test(sy, sx, gy, gx) {
    var r, c, sy, sx, gy, gx,q;
    r = H;
    c = W;
    var maze = input;
    var ds = [0, 1, 0, -1, 0];
    var queue = [[0, sy, sx]];
    var visited = new Array(r * c); // 
    for(var i=0;i<r*c;++i){
      visited[i] = false;
    }
		console.error(r + " " + c);
  	console.error(sy + " " + sx);
  console.error(gy + " " + gx);
    while (queue) {
      myerr(queue);
        q = queue.shift();
      
        if (q[1] === gy && q[2] === gx) {
            //console.log("%d", q[0]);
            return q[0];
        }
        for (var i = 0; i < 4; ++i) {
            var ny = q[1] + ds[i];
            var nx = q[2] + ds[i + 1];
            if (visited[ny * c + nx] === false && maze[ny][nx] === ".") {
                queue.push([q[0] + 1, ny, nx]);
                visited[ny * c + nx] = true;
            }
        }
    }
}


}