#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>
#include <cstring>
using namespace std;
typedef long long LL;
typedef complex<double> 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>
class SCC
{
public:
IdGen<Vert> idgen;
vector< vector<int> > G;
public:
void addVert( Vert s_ )
{
int s = idgen.v2id(s_);
if( s >= G.size() ) G.resize(s+1);
}
void addEdge( Vert s_, Vert t_ )
{
int s = idgen.v2id(s_), t = idgen.v2id(t_);
if( max(s,t) >= G.size() ) G.resize(max(s,t)+1);
G[s].push_back(t);
}
void scc()
{
int N = G.size();
dfs_no.assign(N, 0);
dfs_lo.assign(N, 0);
pending = stack<int>();
scc_id.assign(N, -1);
scc_list.clear();
scc_children.clear();
for(int v=0; v<N; ++v)
dfs(v);
}
vector<int> scc_id; // which scc does the vert belong to?
vector< vector<int> > scc_list; // list of nodes in the scc
vector< vector<int> > scc_children; // forest relationship of sccs
private:
int no;
vector<int> dfs_no; // 1-origin dfs-visit ID
vector<int> dfs_lo; // the least ID in the vert's scc
stack<int> pending; // current unclassigied verts
void dfs(int v)
{
// visit v if not yet
if( dfs_no[v] )
return;
dfs_no[v] = dfs_lo[v] = ++no;
pending.push(v);
// visit children
for(int i=0; i<G[v].size(); ++i) {
int u = G[v][i];
dfs( u );
if( scc_id[u] == -1 )
dfs_lo[v] = min( dfs_lo[v], dfs_lo[u] );
}
// when v is the representative of scc
if( dfs_no[v] == dfs_lo[v] ) {
vector<int> scc;
for(;;) {
int w = pending.top(); pending.pop();
scc.push_back(w);
scc_id[w] = scc_list.size();
if( w == v ) break;
}
scc_list.push_back(scc);
set<int> children;
for(int j=0; j<scc.size(); ++j)
for(int i=0; i<G[scc[j]].size(); ++i)
children.insert( scc_id[G[scc[j]][i]] );
children.erase(scc_id[v]);
scc_children.push_back( vector<int>(children.begin(), children.end()) );
}
}
};
class ImpossibleGame { public:
static LL C(LL n, LL k) {
LL v = 1;
for(int i=1; i<=k; ++i)
v = v * (n+1-i) / i;
return v;
}
static LL weight(LL a, LL b, LL c, LL d) {
return C(a+b+c+d,a) * C(b+c+d,b) * C(c+d,c);
}
long long getMinimum(int k, vector <string> before, vector <string> after)
{
vector< pair< vector<int>, vector<int> > > dif;
for(int i=0; i<after.size(); ++i)
{
vector<int> be(4), af(4);
for(int j=0; j<before[i].size(); ++j) be[before[i][j]-'A'] ++;
for(int j=0; j< after[i].size(); ++j) af[ after[i][j]-'A'] ++;
dif.push_back( make_pair(be,af) );
}
SCC< vector<int> > G;
vector<int> v(4);
for(v[0]=0; v[0]<=k; ++v[0])
for(v[1]=0; v[0]+v[1]<=k; ++v[1])
for(v[2]=0; v[0]+v[1]+v[2]<=k; ++v[2])
{
v[3] = k - v[0] - v[1] - v[2];
G.addVert(v);
for(int i=0; i<dif.size(); ++i)
{
bool dame = false;
vector<int> u = v;
for(int k=0; k<4; ++k)
{
if( (u[k]-=dif[i].first[k]) < 0 )
dame = true;
u[k] += dif[i].second[k];
}
if( !dame )
G.addEdge(v, u);
}
}
G.scc();
LL ans = 0;
for(int v=0; v<G.scc_list.size(); ++v)
ans = max(ans, rec(v, G));
return ans;
}
map<int, LL> memo;
LL rec(int v, SCC< vector<int> >& G)
{
if( memo.count(v) )
return memo[v];
LL mx = 0;
for(int i=0; i<G.scc_children[v].size(); ++i)
mx = max(mx, rec(G.scc_children[v][i], G));
for(int i=0; i<G.scc_list[v].size(); ++i) {
const vector<int>& str = G.idgen.id2v(G.scc_list[v][i]);
mx += weight(str[0], str[1], str[2], str[3]);
}
return memo[v] = mx;
}
};
// 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 long long& Expected, const long long& 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(_, ImpossibleGame().getMinimum(k, before, after));}
int main(){
CASE(0)
int k = 1;
string before_[] = { "A" };
vector <string> before(before_, before_+sizeof(before_)/sizeof(*before_));
string after_[] = { "B" };
vector <string> after(after_, after_+sizeof(after_)/sizeof(*after_));
long long _ = 2LL;
END
CASE(1)
int k = 2;
string before_[] = { "A", "A", "D" };
vector <string> before(before_, before_+sizeof(before_)/sizeof(*before_));
string after_[] = { "B", "C", "D" };
vector <string> after(after_, after_+sizeof(after_)/sizeof(*after_));
long long _ = 5LL;
END
CASE(2)
int k = 2;
string before_[] = { "B", "C", "D" };
vector <string> before(before_, before_+sizeof(before_)/sizeof(*before_));
string after_[] = { "C", "D", "B" };
vector <string> after(after_, after_+sizeof(after_)/sizeof(*after_));
long long _ = 9LL;
END
CASE(3)
int k = 6;
string before_[] = { "AABBC", "AAAADA", "AAACA", "CABAA", "AAAAAA", "BAAAA" };
vector <string> before(before_, before_+sizeof(before_)/sizeof(*before_));
string after_[] = { "AACCB", "DAAABC", "AAAAD", "ABCBA", "AABAAA", "AACAA" };
vector <string> after(after_, after_+sizeof(after_)/sizeof(*after_));
long long _ = 499LL;
END
CASE(4)
int k = 7;
string before_[] = {"BDBBB", "ACBBBBC", "BBBBC", "CCACCCB", "CC", "BBBBBBD", "BBDBBAB", "DBBCBB", "DBABABB", "BBBBABB", "BBBBB", "BBABB", "BBBBBDB", "ABDC", "BDBBDCB", "BBBBBAC", "BBBDBC", "BBBBBBA", "BBBBBBB", "BACCBB", "ABBDABB", "DC", "ABBDBB", "ACBCABB"};
vector <string> before(before_, before_+sizeof(before_)/sizeof(*before_));
string after_[] = {"BADBC", "ACDBCBB", "BADCB", "BBBDBBC", "BD", "BBACCBD", "BBADBDB", "BBBBCC", "BBBCBBB", "BCBDCBD", "ABBBA", "DDBAB", "BCBDBDB", "BBCB", "BBCBBBB", "BABCBDB", "BBCCBD", "BBBBBCB", "DBCBADC", "BBBACA", "ABBABBC", "DB", "DBBCBB", "BBDBBBB"};
vector <string> after(after_, after_+sizeof(after_)/sizeof(*after_));
long long _ = 7112LL;
END
/*
CASE(5)
int k = ;
string before_[] = ;
vector <string> before(before_, before_+sizeof(before_)/sizeof(*before_));
string after_[] = ;
vector <string> after(after_, after_+sizeof(after_)/sizeof(*after_));
long long _ = LL;
END
*/
}
// END CUT HERE