#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <memory>
#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;
template<typename T>
class IdGen
{
map<T, int> v2id_;
vector<T> id2v_;
public:
int v2id(const T& v) {
if( !v2id_.count(v) ) { v2id_[v] = size(); id2v_.push_back(v); }
return v2id_[v];
}
const T& id2v(int i) const { return id2v_[i]; }
int size() const { return id2v_.size(); }
};
template<typename Vert, typename Flow, int NV=512>
class MaxFlow
{
IdGen<Vert> idgen;
vector<int> G[NV];
Flow F[NV][NV];
public:
void addEdge( Vert s_, Vert t_, Flow f )
{
const int s = idgen.v2id(s_), t = idgen.v2id(t_);
G[s].push_back(t);
G[t].push_back(s);
F[s][t] = f;
F[t][s] = 0;
}
Flow calc( Vert s_, Vert t_ )
{
const int S = idgen.v2id(s_), D = idgen.v2id(t_);
for( Flow total=0 ;; ) {
// Do BFS and compute the level for each node.
int LV[NV] = {0};
vector<int> Q(1, S);
for(int lv=1; !Q.empty(); ++lv) {
vector<int> Q2;
for(size_t i=0; i!=Q.size(); ++i) {
const vector<int>& ne = G[Q[i]];
for(size_t j=0; j!=ne.size(); ++j)
if( F[Q[i]][ne[j]] && !LV[ne[j]] && ne[j]!=S )
LV[ne[j]]=lv, Q2.push_back(ne[j]);
}
Q.swap(Q2);
}
// Destination is now unreachable. Done.
if( !LV[D] )
return total;
// Iterating DFS.
bool blocked[NV] = {};
total += dinic_dfs( S, D, LV, 0x7fffffff, blocked );
}
}
private:
Flow dinic_dfs( int v, int D, int LV[], Flow flow_in, bool blocked[] )
{
Flow flow_out = 0;
for(size_t i=0; i!=G[v].size(); ++i) {
int u = G[v][i];
if( LV[v]+1==LV[u] && F[v][u] ) {
Flow f = min(flow_in-flow_out, F[v][u]);
if( u==D || !blocked[u] && (f=dinic_dfs(u,D,LV,f,blocked))>0 ) {
F[v][u] -= f;
F[u][v] += f;
flow_out += f;
if( flow_in == flow_out ) return flow_out;
}
}
}
blocked[v] = (flow_out==0);
return flow_out;
}
};
class DancingParty { public:
int maxDances(vector <string> likes, int k)
{
const int n = likes.size();
for(int M=1; M<=n; ++M) {
typedef pair<int,int> Vert;
auto_ptr< MaxFlow<Vert, int> > mf(new MaxFlow<Vert, int>);
for(int i=0; i<n; ++i) {
mf->addEdge(Vert(0,0), Vert(1,i), M); // src L
mf->addEdge(Vert(1,i), Vert(2,i), M); // L YL
mf->addEdge(Vert(1,i), Vert(3,i), k); // L NL
mf->addEdge(Vert(4,i), Vert(6,i), M); // YR R
mf->addEdge(Vert(5,i), Vert(6,i), k); // NR R
mf->addEdge(Vert(6,i), Vert(7,0), M); // R dst
for(int j=0; j<n; ++j)
if( likes[i][j] == 'Y' )
mf->addEdge(Vert(2,i), Vert(4,j), 1);
else
mf->addEdge(Vert(3,i), Vert(5,j), 1);
}
if( mf->calc(Vert(0,0), Vert(7,0)) < M*n )
return M-1;
}
return n;
}
};
// 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(_, DancingParty().maxDances(likes, k));}
int main(){
CASE(0)
string likes_[] = {"YYY", "YYY", "YYY"};
vector <string> likes(likes_, likes_+sizeof(likes_)/sizeof(*likes_));
int k = 0;
int _ = 3;
END
CASE(1)
string likes_[] = {"YYY", "YYN", "YNY"};
vector <string> likes(likes_, likes_+sizeof(likes_)/sizeof(*likes_));
int k = 0;
int _ = 2;
END
CASE(2)
string likes_[] = {"YN", "YN"};
vector <string> likes(likes_, likes_+sizeof(likes_)/sizeof(*likes_));
int k = 0;
int _ = 0;
END
CASE(3)
string likes_[] = {"YN", "YN"};
vector <string> likes(likes_, likes_+sizeof(likes_)/sizeof(*likes_));
int k = 1;
int _ = 1;
END
/*
CASE(4)
string likes_[] = ;
vector <string> likes(likes_, likes_+sizeof(likes_)/sizeof(*likes_));
int k = ;
int _ = ;
END
CASE(5)
string likes_[] = ;
vector <string> likes(likes_, likes_+sizeof(likes_)/sizeof(*likes_));
int k = ;
int _ = ;
END
*/
}
// END CUT HERE