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 Rust (1.42.0) (judge verdict: Accepted)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};
 
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };
 
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
 
    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };
 
    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };
 
    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };
 
    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
 
use std::cmp::Ordering;
use std::cmp;
use std::cmp::min;
use std::collections::BTreeMap;
use std::process;
use std::cmp::Ord;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::VecDeque;
use std::collections::BTreeSet;
use std::mem;
use std::collections::BinaryHeap;
use std::hash::{Hash, Hasher};

// ---------- begin ModInt ----------

#[derive(Clone, Copy)]
struct ModInt(usize);
impl std::ops::Add for ModInt {
    type Output = ModInt;
    fn add(self, rhs: ModInt) -> Self::Output {
        let mut d = self.0 + rhs.0;
        if d >= MODu {
            d -= MODu;
        }
        ModInt(d)
    }
}

impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, rhs: ModInt) {
        *self = *self + rhs;
    }
}

impl std::ops::Sub for ModInt {
    type Output = ModInt;
    fn sub(self, rhs: ModInt) -> Self::Output {
        let mut d = self.0 + MODu - rhs.0;
        if d >= MODu {
            d -= MODu;
        }
        ModInt(d)
    }
}

impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: ModInt) {
        *self = *self - rhs;
    }
}

impl std::ops::Mul for ModInt {
    type Output = ModInt;
    fn mul(self, rhs: ModInt) -> Self::Output {
        ModInt((self.0 as u64 * rhs.0 as u64 % MODu as u64) as usize)
    }
}

impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: ModInt) {
        *self = *self * rhs;
    }
}

impl std::ops::Neg for ModInt {
    type Output = ModInt;
    fn neg(self) -> Self::Output {
        ModInt(if self.0 == 0 {0} else {MODu - self.0})
    }
}

impl std::fmt::Display for ModInt {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl std::str::FromStr for ModInt {
    type Err = std::num::ParseIntError;
    fn from_str(s: &str) -> Result<Self, Self::Err> {
        let val = s.parse::<usize>()?;
        Ok(ModInt::new(val))
    }
}
impl PartialEq for ModInt {
    fn eq(&self, other: &Self) -> bool {
        self.0 == other.0
    }
}
impl Hash for ModInt {
    fn hash<H: Hasher>(&self, state: &mut H) {
        self.0.hash(state);
        self.0.hash(state);
    }
}
impl Eq for ModInt {}
#[allow(dead_code)]
impl ModInt {
    pub fn new(n: usize) -> ModInt {
        ModInt(n % MODu)
    }
    pub fn zero() -> ModInt {
        ModInt(0)
    }
    pub fn one() -> ModInt {
        ModInt(1)
    }
    pub fn pow(self, mut n: usize) -> ModInt {
        let mut t = ModInt::one();
        let mut s = self;
        while n > 0 {
            if n & 1 == 1 {
                t *= s;
            }
            s *= s;
            n >>= 1;
        }
        t
    }
    pub fn inv(self) -> ModInt {
        self.pow(MODu - 2)
    }
}
// ---------- end ModInt ----------

/// Equivalent to std::lowerbound and std::upperbound in c++
pub trait BinarySearch<T> {
    fn lower_bound(&self, x:&T) -> usize;
    fn upper_bound(&self, x:&T) -> usize;
}
 
impl<T: Ord> BinarySearch<T> for VecDeque<T>{
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
 
    fn upper_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less | Ordering::Equal => {
                    low = mid + 1;
                }
                Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}
impl<T: Ord> BinarySearch<T> for [T]{
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
 
    fn upper_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less | Ordering::Equal => {
                    low = mid + 1;
                }
                Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}

fn matmul(A:&Vec<Vec<i64>>, B:&Vec<Vec<i64>>) -> Vec<Vec<i64>>{
    let mut C = vec![vec![0;B[0].len()];A.len()];
    for i in 0..A.len(){
        for k in 0..B.len(){
            for j in 0..B[0].len(){
                C[i][j] += A[i][k]*B[k][j];
                C[i][j] %= MOD;
            }
        }
    }
    return C;
}
fn matpow(A:&mut Vec<Vec<i64>>, n:usize) -> Vec<Vec<i64>>{
    let mut B = vec![vec![0;A.len()];A.len()];
    for i in 0..A.len(){
        B[i][i] = 1;
    }
    let mut n = n;
    let mut tmp = A.clone();
    while(n>0){
        if n&1 == 1{B = matmul(&B, &tmp);}
        tmp = matmul(&tmp, &tmp);
        n>>=1;
    }
    return B;
}

 
 
 

fn divisor(n:usize) -> Vec<usize>{
    let mut res:Vec<usize> = Vec::new(); 
    for i in 1..n+1{
        if i*i>n{break;}
        if n%i == 0{
            res.push(i);
            if i != n/i{
                res.push(n/i);    
            }    
        }    
    }
    res
}
struct UnionFind{
    par:Vec<usize>,
    rank:Vec<usize>,
    size:Vec<usize>,
    size_edge:Vec<usize>,
}
impl UnionFind{
    fn init(n:usize) -> UnionFind{
        let mut par = vec![0;n];
        for i in 0..n{
            par[i] = i;
        }
        UnionFind{
            par:par,
            rank:vec![0;n],
            size:vec![1;n],
            size_edge:vec![0;n],
        }
    }
    fn find(&mut self, x:usize) ->usize{
        if(self.par[x] == x){
            x
        }
        else{
            let p = self.par[x];
            let res = self.find(p);
            self.par[x] = res;
            res
        }
    }
    fn same(&mut self, a:usize, b:usize)->bool{
        self.find(a) == self.find(b)
    }
    fn unite(&mut self, a:usize, b:usize){
        let x = self.find(a);
        let y = self.find(b);
        if x != y{
            if (self.rank[x] < self.rank[y]){
                self.par[x] = y;
                self.size[y] += self.size[x];
                self.size_edge[y] += self.size_edge[x];
                self.size_edge[y] += 1;
            }
            else{
                self.par[y] = x;
                self.size[x] += self.size[y];
                self.size_edge[x] += self.size_edge[y];
                self.size_edge[x] += 1;
                if(self.rank[x] == self.rank[y]){ self.rank[x]+=1;}
            }
            
        }
        else{
            self.size_edge[x] += 1;
        }
    }
    fn check_size(&mut self, a:usize) -> usize{
        let x = self.find(a);
        let s = self.size[x];
        s
    }
}
pub struct Scanner<R> {
    stdin: R,
}
 
impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r')
            .collect::<Vec<_>>();
        std::str::from_utf8(&buf).unwrap()
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}
struct LazySegTree<BiOp> {
    n: usize,
    val: Vec<i64>,
    ma:Vec<i64>,
    op: BiOp,
    e: i64,
    upe:i64,
    inf:i64,
}

impl<BiOp> LazySegTree<BiOp>
    where BiOp: Fn(i64, i64) -> i64{
    pub fn new(n_: usize, op: BiOp, e: i64, upe:i64, inf:i64) -> Self {
        let mut n = 1;
        while n < n_ { n *= 2; } // n is a power of 2

        LazySegTree {n: n, val: vec![e; 2 * n ], ma:vec![upe;2*n], op: op, e: e, upe:upe, inf:inf}
    }
    pub fn query(&self, x:usize, y:usize, l:usize, r:usize, k:usize) -> i64 {
        if (r<=x || y<=l) {return self.inf;}
        if (x<=l && r<=y) {return self.ma[k];}
        let mut L = self.query(x,y,l,(l+r)/2, k*2);
        let mut R = self.query(x,y,(l+r)/2,r, k*2+1);
        return self.val[k] + (self.op)(L, R);

    }
    
    pub fn update(&mut self, x:usize, y:usize, v:i64, l:usize,r:usize, k:usize) {
        if (l>=r) {return;}
        if (x<=l && r<=y){
            self.val[k]+=v;
            self.ma[k]+=v;
        }
        else if(l<y && x<r){
            self.update(x, y, v, l, (l+r)/2, k*2);
            self.update(x,y,v,(l+r)/2,r, k*2+1);
            self.ma[k] = self.val[k] + (self.op)(self.ma[k*2], self.ma[k*2+1]);
        }
    }
}
fn modinv(a:ModInt)->ModInt{
    let mut a = a.0 as usize;
    let mut b = MODu as i64;
    let mut u = 1 as i64;
    let mut v = 0 as i64;
    let mut a = a as i64;
    let mut m = MODu as i64;
    while(b>0){
        let mut t = a/b;
        a -= t*b;
        mem::swap(&mut a, &mut b);
        u-=t*v;
        mem::swap(&mut u, &mut v);    
    }
    u%=m;
    if u<0{u+=m;}
    return ModInt(u as usize);

}
fn modinv2(a:usize)->usize{
    let mut a = a as usize;
    let mut b = MODu as i64;
    let mut u = 1 as i64;
    let mut v = 0 as i64;
    let mut a = a as i64;
    let mut m = MODu as i64;
    while(b>0){
        let mut t = a/b;
        a -= t*b;
        mem::swap(&mut a, &mut b);
        u-=t*v;
        mem::swap(&mut u, &mut v);
    }
    u%=m;
    if u<0{u+=m;}
    return u as usize;

}
fn modpow(x:ModInt, n:ModInt) -> ModInt{
        let mut ans = ModInt(1);
        let mut n = n.0 as usize;
        let mut x = x;
        while(n != 0){
            if (n&1 == 1){ans = ans*x;}
            x = x*x;
            n = n>>1;
        }
        ans
}
fn comb(a:usize, b:usize,  fac:&Vec<ModInt>, ifac:&Vec<ModInt>)->ModInt{
        let mut a = a;
        let mut b = b;
        if a == 0 && b == 0{return ModInt(1);}
        if a<b || a<0{return ModInt(0);}
        let mut tmp = ifac[a-b]*ifac[b];
        return tmp * fac[a];
}

fn invs()->(Vec<ModInt>, Vec<ModInt>){
    let mut fac = vec![ModInt(0);600001];
    let mut ifac = vec![ModInt(0);600001];
    fac[0] = ModInt(1);
    ifac[0] = ModInt(1);
    for i in 0..600000{

        fac[i+1] = fac[i] * ModInt(i+1);
        ifac[i+1] = ifac[i] * modpow(ModInt(i+1), ModInt(MODu - 2));
    }
    (fac, ifac)
}

struct ConvexHallTrick {
    Q: Vec<(i64, i64)>,
}

impl ConvexHallTrick{
    pub fn new() -> Self {

        ConvexHallTrick {Q: Vec::new()}
    }
    pub fn calc(&self, p:(i64, i64), x:i64)->i64{
        return p.0 * x + p.1;
    }
    pub fn dodo(& self, A:(i64, i64), B:(i64, i64), C:(i64, i64)) -> bool{
        //max or min
        (A.1 - C.1) * (B.0 - A.0) <= (A.1 - B.1)*(C.0 - A.0)
    }
    pub fn add(&mut self, a:i64, b:i64){
        self.Q.push((a, b));
        let mut v = self.Q.len();
        while(v >=3 && self.dodo(self.Q[v-3], self.Q[v-2], self.Q[v-1])){
            self.Q[v-2] = self.Q[v-1];
            self.Q.pop();
            v = self.Q.len();
        }
    }
    pub fn query(& self, x:i64) -> i64{
        let mut L = -1;
        let mut R = (self.Q.len() - 1) as i64;
        while(R-L>1){
            let mut m = (L+R)/2;
            if self.calc(self.Q[m as usize], x)>=self.calc(self.Q[m as usize+1], x){
                L=m;
            }
            else{
                R=m;
            }

        }
        return self.calc(self.Q[R as usize], x);
    }
}
#[derive(Eq, PartialEq, Clone, Debug)]
pub struct Rev<T>(pub T);
impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}
impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}
fn sieve(n:usize) -> (Vec<bool>, Vec<usize>){
    let mut p:usize = 0;
    let mut is_prime = vec![false; n+1];
    let mut prime = Vec::new();
    for i in 0..n+1{
        is_prime[i] = true;
    }
    is_prime[0] = false;
    is_prime[1] = false;
    for i in 2..n+1{
        if is_prime[i]{
            prime.push(i as usize);
            let mut j = 2*i;
            while(j<=n){
                is_prime[j] = false;
                j+=i;
            }
        }
    }
    (is_prime, prime)
    
}
fn nHr(n:usize, r:usize, fac:&Vec<ModInt>, ifac:&Vec<ModInt>) -> ModInt{
    comb(n + r - 1, r, fac, ifac)
}
fn gcd(a:usize, b:usize)->usize{
    if b==0{return a;}
    return gcd(b, a%b);
}
fn lcm(a:usize, b:usize)->usize{
    return (b/gcd(a, b))*a;
}
struct SegTree_MOD<BiOp> {
    n: usize,
    dat: Vec<i64>,
    op: BiOp,
    e: i64,
    mod_:i64,
}
impl<BiOp> SegTree_MOD<BiOp>
    where BiOp: Fn(i64, i64) -> i64 
          {
    pub fn new(n_: usize, op: BiOp, e: i64, mod_:i64) -> Self {
        let mut n = 1;
        while n < n_ { n *= 2; } // n is a power of 2
        SegTree_MOD {n: n, dat: vec![e; 2 * n - 1], op: op, e: e, mod_:mod_}
    }
    /* ary[k] <- v */
    pub fn update(&mut self, idx: usize, v: i64) {
        let mut k = idx + self.n - 1;
        self.dat[k] = v;
        while k > 0 {
            k = (k - 1) / 2;
            self.dat[k] = (self.op)(self.dat[2 * k + 1], self.dat[2 * k + 2]);
            self.dat[k] %= self.mod_;
        }
    }
    /* [a, b) (note: half-inclusive)
     * http://proc-cpuinfo.fixstars.com/2017/07/optimize-segment-tree/ */
    pub fn query(&self, mut a: usize, mut b: usize) -> i64 {
        let mut left = self.e;
        let mut right = self.e;
        a += self.n - 1;
        b += self.n - 1;
        while a < b {
            if (a & 1) == 0 {
                left = (self.op)(left, self.dat[a]);
                left %= self.mod_;
            }
            if (b & 1) == 0 {
                right = (self.op)(self.dat[b - 1], right);
                right %= self.mod_;
            }
            a = a / 2;
            b = (b - 1) / 2;
        }
        let mut res = (self.op)(left, right);
        res %= self.mod_;
        res
        
    }
}
fn modpow2(x:usize, n:usize) -> usize{
        let mut ans = 1;
        let mut n = n;
        let mut x = x;
        while(n != 0){
            if (n&1 == 1){ans = ans*x%MODu;}
            x = x*x%MODu;
            n = n>>1;
        }
        ans
}
#[derive(Clone)]
struct PPUnionFind{
    par:Vec<usize>,
    rank:Vec<usize>,
    time:Vec<usize>,
    now:usize,
    history:Vec<(usize, usize)>,
}
impl PPUnionFind{
    fn init(n:usize) -> PPUnionFind{
        let mut par = vec![0;n];
        for i in 0..n{
            par[i] = i;
        }
        PPUnionFind{
            par:par,
            rank:vec![0;n],
            time:vec![INF as usize;n],
            now:0,
            history:vec![],
        }
    }
    fn find(&mut self, t:usize, x:usize) ->usize{
        if self.time[x] > t{return x;}
        else { let tt = self.par[x]; return self.find(t, tt);}
    }
    fn unite(&mut self, x:usize, y:usize) -> usize{
        self.now+=1;
        let mut x = x;
        let mut y = y;
        let nc = self.now;
        x = self.find(nc, x);
        y = self.find(nc, y);
        if x == y{return self.now;}
        if self.par[x] < self.par[y] {mem::swap(&mut x, &mut y);}
        self.par[x] += self.par[y];
        self.history.push((self.now, self.par[x]));
        self.par[y] = x;
        self.time[y] = self.now;
        return self.now;
    }
}

fn prim(cost:&Vec<Vec<(usize, i64)>>, vs:usize)->i64{
    let mut used = vec![false; vs];
    let mut bh = BinaryHeap::new();
    for j in 0..cost[0].len(){
            bh.push((cost[0][j].1 * -1, cost[0][j].0));
    }
    used[0] = true;
    let mut res = 0;
    while(bh.len()!=0){
        let mut m = bh.pop().unwrap();
        if used[m.1]{continue;}
        used[m.1] = true;
        for e in 0..cost[m.1].len(){
            if used[cost[m.1][e].0] == false{
                bh.push((cost[m.1][e].1 * -1, cost[m.1][e].0));
            }
        }
        res += m.0*-1;
    }
    return res;
}
fn kruscal(cost:&mut Vec<(i64, usize, usize)>, vs:usize)->i64{
    cost.sort();
    let mut uf = UnionFind::init(vs);
    let mut res = 0;

    for i in 0..cost.len(){
        let e = cost[i].clone();
        if uf.find(e.1) != uf.find(e.2){
            uf.unite(e.1, e.2);
            res += e.0;
        }
    }
    return res;
}
fn kruscal3(cost:&mut Vec<(f64, usize, usize, usize)>, vs:usize)->(UnionFind, Vec<usize>) {
    cost.sort_by(|a, b| (&a.0).partial_cmp(&b.0).unwrap());
    let mut uf = UnionFind::init(vs);
    let mut res = 0.0;
    let mut rv = Vec::new();
    let mut c = 0.0;
    let mut t = 0.0;
    for i in 0..cost.len(){
        let e = cost[i].clone();
        if uf.find(e.1) != uf.find(e.2){
            uf.unite(e.1, e.2);
            rv.push(e.3);
        }
    }
    return (uf,rv);
}
fn kruscal2(cost:&mut Vec<(f64, usize, usize)>, vs:usize)->f64{
    cost.sort_by(|a, b| (&a.0).partial_cmp(&b.0).unwrap());
    let mut uf = UnionFind::init(vs);
    let mut res = 0.0;
    for i in 0..cost.len(){
        let e = cost[i].clone();
        if uf.find(e.1) != uf.find(e.2){
            uf.unite(e.1, e.2);
            res+= e.0;
        }
    }
    return res;
}

struct segtree<I, Op>{
    n: usize,
    dat: Vec<I>,
    op:Op,
    e:I,
}
impl<I, Op> segtree<I, Op>


    where Op: Fn(I, I) -> I, I:Copy{
        
        pub fn new(n_:usize, op: Op, e:I)->Self{
            let mut n = 1;
            while(n<n_){n*=2;}
            segtree{n: n, dat:vec![e; 2*n-1], op:op, e:e}
        }
        pub fn update(&mut self, k:usize, a:I){
            let mut k = k;
            k += self.n-1;
            self.dat[k] = a;
            while(k>0){
                k = (k-1)/2;
                self.dat[k] = (self.op)(self.dat[k*2 + 1], self.dat[k*2+2]);
            }
        }
        pub fn query(&self, a:usize, b:usize, k:usize, l:usize, r:usize) -> I{
            if r<=a || b<=l{return self.e;}
            if a<=l && r<=b{return self.dat[k];}
            else{
                let mut vl = self.query(a, b, k*2+1, l, (l+r)/2);
                let mut vr = self.query(a, b, k*2+2, (l+r)/2, r);
                return (self.op)(vl, vr);
            }
        }
    }
struct BIT<I, Op>{
    n:usize,
    bit:Vec<I>,
    op:Op,
    e:I,
    ini:I,
}
impl <I, Op>  BIT<I, Op>
    /* 1-index*/  
    where Op: Fn(I, I) -> I, I:Copy{
        pub fn new(n_:usize, op:Op, e:I, ini:I)->Self{
            BIT{n:n_, bit:vec![e;n_+1], op:op, e:e, ini:ini}
        }
        pub fn sum(&self, i:usize)->I{
            let mut s = self.ini;
            let mut i = i as i64;
            while(i>0){
                s = (self.op)(s, self.bit[i as usize]);
                i -= i & -i;
            }
            return s;
        }
        pub fn add(&mut self, i:usize, x:I){
            let mut i = i as i64;
            while(i<=self.n as i64){
                self.bit[i as usize] = (self.op)(self.bit[i as usize], x);
                i += i & -i;
            }
        }
    }
struct Dsegtree{
    n: usize,
    datA: Vec<i64>,
    datB:Vec<i64>,
    e:i64,
}
impl Dsegtree{
        pub fn new(n_:usize, e:i64)->Self{

            Dsegtree{n:n_, datA:vec![e; 1<<22 - 1], datB:vec![e;1<<22 - 1], e:e}
        }
        pub fn update(&mut self,a:usize, b:usize, x:i64,  k:usize, l:usize, r:usize){
            //println!("{} {} {} {} {} {}", a, b, x, k , l, r);
            if a<=l && r<=b{
                self.datA[k] += x;
            }
            else if (l<b && a<r){
                self.datB[k] += (cmp::min(b, r) as i64 - cmp::max(a, l) as i64) * x;
                self.update(a, b, x, k*2+1, l, (l+r)/2);
                self.update(a, b, x, k*2+2, (l+r)/2, r);
            }
        }
        pub fn query(&self, a:usize, b:usize, k:usize, l:usize, r:usize) -> i64{
            if (b<=l || r<=a){
                return 0;
            }
            else if (a<=l && r<=b){
                return self.datA[k] * ((r as i64-l as i64)) + self.datB[k];
            }
            else{
                let mut res = (cmp::min(b, r) as i64 - cmp::max(a, l) as i64)* self.datA[k];
                res += self.query(a, b, k*2+1, l, (l+r)/2);
                res += self.query(a, b, k*2+2, (l+r)/2, r);
                return res;
            }
        }
    }
/*
unwrap_or_else
*/
fn prime_factor(n:usize)->HashMap<usize, usize>{
    let mut res = HashMap::new();
    let mut n = n;
    for i in 2..n{
        if i*i>n{break;}
        while(n%i==0){
            *res.entry(i).or_insert(0)+=1;
            n/=i;
        }
    }
    if n != 1{
        res.insert(n, 1);
    }
    res
}
struct rollinghash{
    base:Vec<i64>,
    Mod:Vec<i64>,
    hash:Vec<Vec<i64>>,
    power:Vec<Vec<i64>>,
}
impl rollinghash{
    pub fn new(s:&Vec<usize>)->Self{
        let mut n = s.len();
        let mut base = vec![1007, 2009];
        let mut hash = vec![vec![0;n+1];2];
        let mut power = vec![vec![1;n+1];2];
        let mut Mod = vec![1000000007, 1000000009];
        for iter in 0..2{
            let mut ht = vec![0;n+1];
            let mut pt = vec![1;n+1];
            for i in 0..n{
                hash[iter][i+1] = (hash[iter][i] * base[iter] + s[i] as i64) % Mod[iter];
                power[iter][i+1] = power[iter][i] * base[iter] % Mod[iter];
            }
        }
        return rollinghash{base:base, Mod:Mod, hash:hash, power:power}
   
    }
    pub fn get(&self, l:usize, r:usize)->(i64, i64){
        let mut res = self.hash[0][r] - self.hash[0][l] * self.power[0][r-l] % self.Mod[0];
        if res<0{
            res += self.Mod[0];
        }
        let mut res2 = self.hash[1][r] - self.hash[1][l] * self.power[1][r-l] % self.Mod[1];
        if res2<0{
            res2 += self.Mod[1];
        }
        return (res, res2);
    }

}
struct LCA{
    G:Vec<Vec<(usize, i64)>>,
    depth:Vec<i64>,
    len:Vec<i64>,
    parent:Vec<Vec<usize>>,
    V:usize,
    logV:usize,
}
impl LCA{
    pub fn new(V:usize, G:&Vec<Vec<(usize, i64)>>)->Self{
        let mut logV = 0;
        while(V>(1<<logV)){logV+=1;}
        return LCA{G:G.clone(), logV:logV, V:V, depth:vec![0;V], len:vec![0;V], parent:vec![vec![INFu;V];logV]}
    }
    pub fn init(&mut self, v:usize, par:usize, d:i64, l:i64){
        self.depth[v] = d;
        self.parent[0][v] = par;
        self.len[v] = l;
        for i in 0..self.G[v].len(){
            let mut w = self.G[v][i].0;
            let mut lc = self.G[v][i].1;
            if w == par{continue;}
            self.init(w, v, d+1, lc+l);
        }
    }
    pub fn build(&mut self, root:usize){
        self.init(root, INFu, 0, 0);
        for k in 0..(self.logV-1){
            for v in 0..self.V{
                if self.parent[k][v] == INFu{
                    self.parent[k+1][v] = INFu;
                }
                else{
                    self.parent[k+1][v] = self.parent[k][self.parent[k][v]];
                }
            }
        }
    }
    pub fn lca(&self, u:usize, v:usize)->usize{
        let mut u = u;
        let mut v = v;
        if self.depth[u]>self.depth[v]{
            mem::swap(&mut u, &mut v);
        }
        for k in 0..self.logV{
            if ((self.depth[v]-self.depth[u]) >> k) & 1 == 1{
                v = self.parent[k][v];
            }
        }
        if u == v{
            return u;
        }
        for k in (0..self.logV).rev(){
            if self.parent[k][u] != self.parent[k][v]{
                u = self.parent[k][u];
                v = self.parent[k][v];
            }
        }
        return self.parent[0][u];
    }
    pub fn dist(&self, u:usize, v:usize)->i64{
        let z = self.lca(u, v);
        return self.len[u]+self.len[v]-2*self.len[z];
    }
}



fn fast_prime_factor_table(ma:usize)->Vec<usize>{
    let mut p = sieve(1001);
    let mut minf = vec![0;ma];
    for j in 0..p.1.len(){
        let P = p.1[j];
        let mut now = P;
        for i in 2..ma{
            if minf[now] ==0{
                minf[now] = P;
            }
            now+=P;
            if now>=ma{
                break;
            }
        }
    }
    return minf;
}
fn area_rectanble(x1:f64, x2:f64, x3:f64, y1:f64, y2:f64, y3:f64)->f64{
    let tmp = x1*y2 + x2*y3 + x3*y1 - y1*x2 - y2*x3 - y3*x1;
    tmp.abs()/2.0
}
#[derive(PartialEq, Clone)]
struct FW(f64);

impl Eq for FW {}

impl PartialOrd for FW {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        self.0.partial_cmp(&other.0)
    }
}

impl Ord for FW {
    fn cmp(&self, other: &FW) -> Ordering {
        other.partial_cmp(self).unwrap()

    }
}
/* parsing
    fn expr(s:&Vec<char>, i:&mut usize) -> Vec<usize>{
        let mut val = term(s, i);
        while(*i<s.len() && (s[*i] == '+' || s[*i] == '-')){
            let mut op = encode(s[*i]);
            *i+=1;
            let mut val2 = term(s, i);
            val = cal(val, val2, op);
        }
        return val;
    }
    fn term(s:&Vec<char>, i:&mut usize) -> Vec<usize>{
        let mut val = factor(s, i);
        while(*i<s.len() && s[*i] == '*'){
            let mut op = encode(s[*i]);
            *i+=1;
            let mut val2 = factor(s, i);
            val = cal(val, val2, op);
        }
        return val;
    }
    fn factor(s:&Vec<char>, i:&mut usize)->Vec<usize>{
        if s[*i] == 'R' || s[*i] == 'S' || s[*i] == 'P' || s[*i] == '?'{
            let mut res = encode(s[*i]);
            *i+=1;
            return res;
        }
        *i+=1;
        let mut ret = expr(s, i);
        *i+=1;
        return ret;
    }
*/
fn matmulf64(A:&Vec<Vec<f64>>, B:&Vec<Vec<f64>>) -> Vec<Vec<f64>>{
    let mut C = vec![vec![0.0;B[0].len()];A.len()];
    for i in 0..A.len(){
        for k in 0..B.len(){
            for j in 0..B[0].len(){
                C[i][j] += A[i][k]*B[k][j];
            }
        }
    }
    return C;
}
//sort_by_key(|a| vec![a[0], -a[1]]);
//v.sort_by(|a, b| a.partial_cmp(b).unwrap());






fn fact_mod(n:usize)->usize {
    let mut  f = 1; 
    for i in 2..n+1{
        f = f * (i % MODu) % MODu;
    }
    return f;
}

fn mod_pow(x:usize, n:usize) ->usize{
    if(n == 0){ return 1;}
    let mut res = mod_pow((x * x) % MODu, n / 2 );
    if(n & 1 == 1){ res = (res * x) % MODu;}
    return res;
}

fn comb2(n:usize, r:usize)->usize {
    let mut n = n;
    let mut r = r;
    if(r > n-r) {r = n-r;}
    if(r == 0) {return 1;}
    let mut a = 1;
    for i in 0..r{
        a = a * ((n-i) % MODu) % MODu;
    }
    let mut b = mod_pow(fact_mod(r), MODu-2);
    return (a % MODu) * (b % MODu) % MODu;
}




struct scc{
    G:Vec<Vec<usize>>,
    rG:Vec<Vec<usize>>,
    vs:Vec<usize>,
    used:Vec<bool>,
    cmp:Vec<usize>,
}
impl scc{
    pub fn new(N:usize, G:&Vec<Vec<usize>>, rG:&Vec<Vec<usize>>)->Self{
        scc{G:G.clone(), rG:rG.clone(), vs:vec![], used:vec![false;N], cmp:vec![0;N]}
    }
    pub fn add_edge(&mut self, from:usize, to:usize){
        self.G[from].push(to);
        self.rG[to].push(from);
    }
    pub fn dfs(&mut self, v:usize){
        self.used[v] = true;
        for i in 0..self.G[v].len(){
            let t = self.G[v][i];
            if !self.used[t]{
                self.dfs(t);
            }
        }
        self.vs.push(v);
    }
    pub fn rdfs(&mut self, v:usize, k:usize){
        self.used[v] = true;
        self.cmp[v] = k;
        for i in 0..self.rG[v].len(){
            let t = self.rG[v][i];
            if !self.used[t]{
                self.rdfs(t, k);
            }
        }
    }
    pub fn scc(&mut self)->usize{
        for v in 0..self.G.len(){
            if !self.used[v]{
                self.dfs(v);
            }
        }
        self.used = vec![false;self.used.len()];
        let mut k = 0;
        for i in (0..self.vs.len()).rev(){
            if !self.used[self.vs[i]]{
                let t = self.vs[i];
                self.rdfs(t, k);
                k+=1;
            }
        }
        k
    }
}


#[macro_use]
fn modpow3(x:usize, n:usize,m:usize) -> usize{
        let mut ans = 1;
        let mut n = n;
        let mut x = x;
        x%=m;
        while(n != 0){
            if (n&1 == 1){ans = ans*x%m;}
            x = x*x%m;
            n = n>>1;
        }
        ans%m
}
fn cal1(x:usize, n:usize, m:usize, h:&mut HashMap<usize, usize>)->usize{
    if h.contains_key(&n){
        return h[&n];
    }
    if n == 1{
        return x;
    }
    if n == 0{
        return 0;
    }
    let mut res = 0;
    let mut a = n/2;
    let mut b = n-a;
    res = cal1(x, b, m, h)%m;
    res = ((res*modpow3((10)%m, a*x.to_string().len(), m)%m)%m + cal1(x, a, m, h)%m)%m;
    h.insert(n, res);
    return res;
}
fn cal2(x:usize, n:usize, m:usize, h:&mut HashMap<usize, usize>, l:usize)->usize{
    if h.contains_key(&n){
        return h[&n];
    }
    if n == 1{
        return x;
    }
    if n == 0{
        return 0;
    }
    let mut res = 0;
    let mut a = n/2;
    let mut b = n-a;
    res = cal2(x, b, m, h, l)%m;
    res = ((res*modpow3((10)%m, a*l, m)%m)%m + cal2(x, a, m, h, l)%m)%m;
    h.insert(n, res);
    return res;
}
fn modinv3(a:usize, m:usize)->usize{
    let mut a = a as usize;
    let mut b = m as i64;
    let mut u = 1 as i64;
    let mut v = 0 as i64;
    let mut a = a as i64;
    let mut m = m as i64;
    while(b>0){
        let mut t = a/b;
        a -= t*b;
        mem::swap(&mut a, &mut b);
        u-=t*v;
        mem::swap(&mut u, &mut v);
    }
    u%=m;
    if u<0{u+=m;}
    return u as usize;

}


fn dijkstra(s:usize, g:&Vec<Vec<(usize, i64)>>)->Vec<i64>{
    let mut dist = vec![INF;g.len()];
    dist[s] = 0;
    let mut h = BinaryHeap::new();
    h.push((0, s));
    while(h.len() != 0){
        let mut t = h.pop().unwrap();
        let mut d = t.0 * -1;
        let mut v = t.1;
        if dist[v]<d{
            continue;
        }
        for i in 0..g[v].len(){
            let n = g[v][i].0;
            let dd = g[v][i].1;
            if dist[n]>d+dd{
                dist[n] = d+dd;
                h.push((dist[n]*-1, n));
            }
        }
    }
    return dist;
}
fn dijkstra2(s:usize, g:&Vec<Vec<(usize, i64)>>)->Vec<i64>{
    let mut dist = vec![INF;g.len()];
    dist[s] = 0;
    let mut h = BinaryHeap::new();
    h.push((0, s));
    while(h.len() != 0){
        let mut t = h.pop().unwrap();
        let mut d = t.0 * -1;
        let mut v = t.1;
        if dist[v]<d{
            continue;
        }
        for i in 0..g[v].len(){
            let n = g[v][i].0;
            let dd = g[v][i].1;
            if dist[n]>d+dd{
                dist[n] = d+dd;
                h.push((dist[n]*-1, n));
            }
        }
    }
    return dist;
}

fn solve(){
    let sssss = std::io::stdin();
    let mut sc = Scanner { stdin: sssss.lock() };
    let mut H:usize = sc.read();
    let mut W:usize = sc.read();
    let mut K:usize = sc.read();
    let mut s = vec![];
    for i in 0..H{
        let mut ss:String = sc.read();
        let mut ss:Vec<char> = ss.chars().collect();
        s.push(ss);
    }
    let mut res = 0;
    for i in 0..1<<H{
        for j in 0..1<<W{
            let mut S = s.clone();
            for ii in 0..H{
                if (i>>ii)&1==1{
                    for jj in 0..W{
                        S[ii][jj] = '.';
                    }
                }
            }

            for ii in 0..W{
                if (j>>ii)&1==1{
                    for jj in 0..H{
                        S[jj][ii] = '.';
                    }
                }
            }
            let mut tmp = 0;
            for ii in 0..H{
                for jj in 0..W{
                    if S[ii][jj] == '#'{
                        tmp +=1;
                    }
                }
            }
            if tmp == K{
                res+=1;
            }


        }
    }
    println!("{}", res);















}

fn main(){
    solve();
}
const PI:f64 = std::f64::consts::PI;
pub static MOD:i64 = 1000000007;
pub static MODu:usize = 1000000007;
pub static MODi32:i32 = 1000000007;
pub static eps:f64 = 1e-6;
const INF: i64 = 1 << 62;
const INFu:usize = 1<<62;