Problem:
Score : 300 points

Problem Statement

We have a grid of H rows and W columns of squares. The color of the square at the i-th row from the top and the j-th column from the left (1 \leq i \leq H, 1 \leq j \leq W) is given to you as a character c_{i,j}: the square is white if c_{i,j} is ., and black if c_{i,j} is #.

Consider doing the following operation:

Choose some number of rows (possibly zero), and some number of columns (possibly zero). Then, paint red all squares in the chosen rows and all squares in the chosen columns.

You are given a positive integer K. How many choices of rows and columns result in exactly K black squares remaining after the operation? Here, we consider two choices different when there is a row or column chosen in only one of those choices.

Constraints

1 \leq H, W \leq 6

1 \leq K \leq HW

c_{i,j} is . or #.

Input

Input is given from Standard Input in the following format:

H W K
c_{1,1}c_{1,2}...c_{1,W}
c_{2,1}c_{2,2}...c_{2,W}
:
c_{H,1}c_{H,2}...c_{H,W}

Output

Print an integer representing the number of choices of rows and columns satisfying the condition.

Sample Input 1

2 3 2
..#
###

Sample Output 1

5

Five choices below satisfy the condition.

The 1-st row and 1-st column

The 1-st row and 2-nd column

The 1-st row and 3-rd column

The 1-st and 2-nd column

The 3-rd column

Sample Input 2

2 3 4
..#
###

Sample Output 2

1

One choice, which is choosing nothing, satisfies the condition.

Sample Input 3

2 2 3
##
##

Sample Output 3

0

Sample Input 4

6 6 8
..##..
.#..#.
#....#
######
#....#
#....#

Sample Output 4

208

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

//↓見なくていいよ！ここから--------------------------------------------------
var read = require('readline').createInterface({
  input: process.stdin,
  output: process.stdout
});
var obj;
var inLine = [];
read.on('line', function(input){inLine.push(input);});
read.on('close', function(){
  obj = init(inLine);
  console.error("\n");
  var start = new Date();
  Main();
  var end = new Date() - start;
  
  myerr("time : " + (end) + "ms");
  myerr("memory : " + Math.round(process.memoryUsage().heapTotal / 1024) + "KB");
});
function nextInt(){return myconv(next(),1);} function nextStrArray(){return myconv(next(),2);}
function nextIntArray(){return myconv(next(),4);} function nextCharArray(){return myconv(next(),6);}
function next(){return obj.next();} function hasNext(){return obj.hasNext();}
function init(input){  
  var returnObj = {
    list : input, index : 0, max : input.length,
    hasNext : function(){return (this.index < this.max);},
    next : function(){if(!this.hasNext()){throw "ArrayIndexOutOfBoundsException これ以上ないよ";}else{var returnInput = this.list[this.index];this.index++;return returnInput;}}
  };
  return returnObj;
}
function myout(s){console.log(s);}
function myerr(s){console.error("debug:" + require("util").inspect(s,false,null));}
//[no]要素の扱い。数値型
//不明値、異常時:引数そのまま返す 1:数値へ変換
//2:半角SPで分割 4:半角SPで分割し、数値配列へ
//6:1文字で分割  7:1文字で分割し、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){try{switch(no){case 1:return parseInt(i);case 2:return i.split(" ");case 4:return i.split(" ").map(Number);case 6:return i.split("");case 7:return i.split("").map(Number);case 8:return i.join(" ");case 9:return i.join("\n");case 0:return i.join("");default:return i;}}catch(e){return i;}}


//↑見なくていいよ！ここまで--------------------------------------------------
function Main(){
	var one = nextIntArray();
	var H = one[0];
	var W = one[1];
	var kK = one[2];
	var list = new Array(H);
	for(var i = 0; i < H; i++){
		list[i] = nextCharArray();
	}
	var output = 0;
	for(var i = 0; i < (1 << H); i++){
		var selectH = [];
	        for(var j = 0; j < H; j++){
	                if((i & (1 << j)) != 0){
				selectH.push(j);
	                        //選ぶ
	                }
	        }
		for(var j = 0; j < (1 << W); j++){
			var selectW = [];
		        for(var k = 0; k < W; k++){
		                if((j & (1 << k)) != 0){
					selectW.push(k);
		                        //選ぶ
		                }
		        }
			var newList = JSON.parse(JSON.stringify(list));
			for(var k = 0; k < selectH.length; k++){
				for(var l = 0; l < W; l++){
					newList[selectH[k]][l] = "*";
				}
			}
			for(var k = 0; k < selectW.length; k++){
				for(var l = 0; l < H; l++){
					newList[l][selectW[k]] = "*";
				}
			}
			var kCount = 0;
			for(var k = 0; k < H; k++){
				for(var l = 0; l < W; l++){
					if(newList[k][l] == "#"){
						kCount++;
					}
				}
			}
			if(kCount == kK){
				output++;
			}
		}
	}
	myout(output);
}