173C.cpp

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*/                              
#include<bits/stdc++.h>
using namespace std;
 
#define fastio ios_base::sync_with_stdio(0); cin.tie(0)
#define LL long long 
#define mod 1000000007 
#define FOR(i, j, k) for (auto i=j ; i<k ; i++)
#define ROF(i, j, k) for (auto i=j ; i>=k ; i--) 
#define debug(...) fprintf(stderr, __VA_ARGS__), fflush(stderr)
#define time__(d) for(long blockTime = 0; (blockTime == 0 ? (blockTime=clock()) != 0 : false); debug("%s time : %.4fs", d, (double)(clock() - blockTime) / CLOCKS_PER_SEC))

const long long INF = 1e18;
const long long MAX = 1e5+10;
int n ,m,k;
LL  f(vector<vector<char>>&a, LL bl, LL cnt,int r, int c) {
    if(bl-cnt==k) return 1;
    if(r>=n || c>=m || bl-cnt<0) return 0;
    int rr=0,cc=0,cm=0;
    FOR(i,0,n) if(a[i][c]=='#') cc++;
    FOR(i,0,m) if(a[r][i]=='#') rr++;
    if(a[r][c]=='#') cm=-1;
    return f(a,bl,cnt+rr,r+1,c) + f(a,bl,cnt+cc,r,c+1) + f(a,bl,cnt+rr+cc+cm,r+1,c+1)
            - f(a,bl,cnt,r+1,c+1)+f(a,bl,cnt,r,c+1)+f(a,bl,cnt,r+1,c);
}
int main(){
    fastio;
    int t=1;// cin>>t;
    while(t--){
       cin>>n>>m>>k; vector<vector<char>>a(n,vector<char>(m));
        int bl=0;
        FOR(i,0,n) FOR(j,0,m) {cin>>a[i][j]; if(a[i][j]=='#') bl++; }
        LL cnt=0;
        FOR(i,0,1<<n )
            FOR(j,0,1<<m ) {
                int rr=0,cc=0,cm=0;
                FOR(r,0,n) {
                    if(i&(1<<r))  {
                        FOR(k,0,m) {if(a[r][k]=='#') rr++; if(j&(1<<k) && a[r][k]=='#' ) cm++; }
                    }
                }                
                FOR(c,0,m) {
                    if(j&(1<<c))  
                      FOR(k,0,n) if(a[k][c]=='#') cc++;
                }  
            if(bl-rr-cc+cm==k) cnt++;
            }
            cout<<cnt;
    }
}