#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
using namespace std;
typedef long long LL;
typedef long double LD;
typedef complex<LD> CMP;
class MagicalHats { public:
int NC, NH, H, W, NG;
vector<int> gain;
vector< pair<int,int> > hats;
vector<int> tate_base, yoko_base;
int findMaximumReward(vector <string> board, vector <int> coins, int numGuesses)
{
NC = coins.size();
sort(coins.begin(), coins.end());
gain.assign(NC+1, 0);
partial_sum(coins.begin(), coins.end(), gain.begin()+1);
H = board.size();
W = board[0].size();
hats.clear();
tate_base.resize(W);
yoko_base.resize(H);
for(int y=0; y<H; ++y)
for(int x=0; x<W; ++x)
if(board[y][x] == 'H') {
hats.push_back( make_pair(y,x) );
tate_base[x]++;
yoko_base[y]++;
}
NH = hats.size();
NG = numGuesses;
int m = 0;
for(int i=0; i<NH; ++i)
m = m*3 + 2;
p_memo.resize(m+1);
p_memo_set.resize(m+1);
b_memo.resize(m+1);
b_memo_set.resize(m+1);
return is_possible(m) ? gain[best_num(m, NG)] : -1;
}
vector<bool> p_memo;
vector<bool> p_memo_set;
bool is_possible(int state)
{
if(p_memo_set[state])
return p_memo[state];
p_memo_set[state] = true;
vector<int> yoko = yoko_base, tate = tate_base, next;
int cnt = 0;
for(int i=0,m=1; i<NH; ++i,m*=3)
{
int v = (state/m)%3;
if( v == 1 ) {
int y = hats[i].first;
int x = hats[i].second;
yoko[y]++;
tate[x]++;
++cnt;
} else if( v == 2 ) {
next.push_back(m);
}
}
if( next.empty() )
{
if( cnt != NC )
return false;
for(int y=0; y<yoko.size(); ++y)
if(yoko[y]%2 != 0)
return p_memo[state] = false;
for(int x=0; x<tate.size(); ++x)
if(tate[x]%2 != 0)
return p_memo[state] = false;
return p_memo[state] = true;
}
else
{
int m = next[0];
int s[] = {state-2*m, state-m};
return p_memo[state] = ( is_possible(s[0]) || is_possible(s[1]) );
}
}
vector<char> b_memo;
vector<bool> b_memo_set;
char best_num(int state, int guess)
{
if( guess==0 )
return 0;
if(b_memo_set[state])
return b_memo[state];
b_memo_set[state] = true;
char best = 0;
for(int i=0,m=1; i<NH; ++i,m*=3)
{
int v = (state/m)%3;
if( v == 2 )
{
int s[] = {state-2*m, state-m};
char score = 13;
if( is_possible(s[0]) )
score = min(score, best_num(s[0], guess-1));
if( is_possible(s[1]) )
score = min<char>(score, best_num(s[1], guess-1)+1);
best = max(best, score);
}
}
return b_memo[state] = best;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const int& Expected, const int& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, MagicalHats().findMaximumReward(board, coins, numGuesses));}
int main(){
CASE(0)
string board_[] = {"H"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int coins_[] = {1};
vector <int> coins(coins_, coins_+sizeof(coins_)/sizeof(*coins_));
int numGuesses = 1;
int _ = 1;
END
CASE(1)
string board_[] = {"HHH",
"H.H",
"HH."};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int coins_[] = {9};
vector <int> coins(coins_, coins_+sizeof(coins_)/sizeof(*coins_));
int numGuesses = 1;
int _ = 9;
END
CASE(2)
string board_[] = {"HH",
"HH"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int coins_[] = {1,2,3,4};
vector <int> coins(coins_, coins_+sizeof(coins_)/sizeof(*coins_));
int numGuesses = 3;
int _ = 6;
END
CASE(3)
string board_[] = {"HHH",
"HHH",
"H.H"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int coins_[] = {13,13,13,13};
vector <int> coins(coins_, coins_+sizeof(coins_)/sizeof(*coins_));
int numGuesses = 2;
int _ = 13;
END
CASE(4)
string board_[] = {"HHH",
"HHH",
"H.H"};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int coins_[] = {13,13,13,13};
vector <int> coins(coins_, coins_+sizeof(coins_)/sizeof(*coins_));
int numGuesses = 3;
int _ = 26;
END
CASE(5)
string board_[] = {"H.H.",
".H.H",
"H.H."};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int coins_[] = {17};
vector <int> coins(coins_, coins_+sizeof(coins_)/sizeof(*coins_));
int numGuesses = 6;
int _ = -1;
END
CASE(6)
string board_[] = {"HHH..........",
"H.H..........",
"HHH..........",
"H.H..........",
"HHH.........."
".............",
".............",
".............",
".............",
".............",
".............",
".............",
".............",
};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int coins_[] = {33,337,1007,2403,5601,6003,9999};
vector <int> coins(coins_, coins_+sizeof(coins_)/sizeof(*coins_));
int numGuesses = 5;
int _ = 1377;
END
CASE(7)
string board_[] = {".............",
".............",
".............",
".............",
".............",
".............",
".....H.H.....",
"......H......",
".....H.H.....",
".............",
".............",
".............",
"............."};
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int coins_[] = {22};
vector <int> coins(coins_, coins_+sizeof(coins_)/sizeof(*coins_));
int numGuesses = 3;
int _ = 22;
END
/*
CASE(8)
string board_[] = ;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int coins_[] = ;
vector <int> coins(coins_, coins_+sizeof(coins_)/sizeof(*coins_));
int numGuesses = ;
int _ = ;
END
CASE(9)
string board_[] = ;
vector <string> board(board_, board_+sizeof(board_)/sizeof(*board_));
int coins_[] = ;
vector <int> coins(coins_, coins_+sizeof(coins_)/sizeof(*coins_));
int numGuesses = ;
int _ = ;
END
*/
}
// END CUT HERE