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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

'''
.append(要素) リストに要素を追加
.extend(リスト) リストを連結する
.insert(場所,要素) 指定した場所に要素追加
del 配列名[場所]
-1で末尾で末尾から一つ前
sort()
sorted(reverse=true)
配列の初期化
配列名=[a]*n+[b]*m
Decimal()
'''

from sys import stdin
from itertools import accumulate, dropwhile, takewhile, groupby
import bisect
import copy
import math
from functools import reduce
from operator import mul
from collections import Counter
import itertools
import fractions
import sys
d = stdin.readline().rstrip().split()
H = int(d[0])
W = int(d[1])
K = int(d[2])

data = []
bCount = 0
result = 0
for el1 in range(H):
    tmp = stdin.readline().rstrip().split()
    d = []
    for el in tmp:
        for el3 in el:
            if el3 == '#':
                bCount += 1
            d.append(el3)
    data.append(d)
datas = copy.deepcopy(data)
counter = 0
for el in range(H+W):
    counter += 2**el
for el in range(counter+1):
    bin_str = ''.join(list(reversed(str(bin(el))[2:])))
    poss = []
    count = 0
    for el2 in bin_str:
        if el2 == '1':
            poss.append(count)
        count += 1
    res = 0
    for el2 in poss:
        if el2 >= H:
            el2 -= H
            for el3 in datas:
                el3[el2] = 'o'
        else:
            datas[el2] = ['o']*W
    for el2 in datas:
        res += el2.count('#')
    if bCount-res == K:
        result += 1
    datas = copy.deepcopy(data)
print(result)