#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;
class PalindromePhrases {
public:
vector<string> W;
int N;
map<pair<int,string>, LL> memo1;
map<pair<int,string>, LL> memo2;
map<pair<int,string>, LL> memo3;
map<pair<int,string>, LL> memo4;
map<pair<int,string>, LL> memo5;
string rev(string s)
{
reverse(s.begin(), s.end());
return s;
}
bool prefix_all(const string& p, const string& a)
{
return p.size() <= a.size() && equal(p.begin(), p.end(), a.begin());
}
bool suffix_all(const string& p, const string& a)
{
return p.size() <= a.size() && equal(p.begin(), p.end(), a.begin()+a.size()-p.size());
}
long long getAmount(vector <string> words)
{
W = words;
N = W.size();
LL cnt = 0;
for(int i=0; i<N; ++i)
{
int mask = (1<<N) - 1;
mask &= ~ (1<<i);
cnt += rec_startpalin(mask, W[i]);
}
return cnt;
}
LL rec_startpalin(int mask, const string& w) // #{ws | ws is palin}
{
pair<int,string> key(mask, w);
if( memo1.count(key) )
return memo1[key];
string rw = rev(w);
LL cnt = 0;
cnt += rec_end(mask, rw);
for(int ov=1; ov<=w.size(); ++ov)
if( w.substr(w.size()-ov) == rw.substr(0,ov) )
cnt += exact(mask, rw.substr(ov));
return memo1[key]=cnt;
}
LL rec_endpalin(int mask, const string& w) // #{sw | sw is palin}
{
pair<int,string> key(mask, w);
if( memo4.count(key) )
return memo4[key];
string rw = rev(w);
LL cnt = 0;
cnt += rec(mask, rw);
for(int ov=1; ov<=w.size(); ++ov)
if( rw.substr(w.size()-ov) == w.substr(0,ov) )
cnt += exact(mask, rw.substr(0,w.size()-ov));
return memo4[key]=cnt;
}
LL rec(int mask, const string& w) // #{ws | s is palin}
{
pair<int,string> key(mask, w);
if( memo2.count(key) )
return memo2[key];
LL cnt = (w.empty() ? 1 : 0);
for(int i=0; i<N; ++i)
if( mask & (1<<i) )
{
if( prefix_all(W[i], w) )
cnt += rec( mask &~ (1<<i),
w.substr(W[i].size())
);
else if( prefix_all(w, W[i]) )
cnt += rec_startpalin( mask &~ (1<<i),
W[i].substr(w.size())
);
}
return memo2[key]=cnt;
}
LL rec_end(int mask, const string& w) // #{sw | s is palin}
{
pair<int,string> key(mask, w);
if( memo5.count(key) )
return memo5[key];
LL cnt = (w.empty() ? 1 : 0);
for(int i=0; i<N; ++i)
if( mask & (1<<i) )
{
if( suffix_all(W[i], w) )
cnt += rec_end( mask &~ (1<<i),
w.substr(0,w.size()-W[i].size())
);
else if( suffix_all(w, W[i]) )
cnt += rec_endpalin( mask &~ (1<<i),
W[i].substr(0, W[i].size()-w.size())
);
}
return memo5[key]=cnt;
}
LL exact(int mask, const string& w) // # of ways to create w
{
pair<int,string> key(mask, w);
if( memo3.count(key) )
return memo3[key];
LL cnt = (w.empty() ? 1 : 0);
for(int i=0; i<N; ++i)
if( mask & (1<<i) )
if( prefix_all(W[i], w) )
cnt += exact( mask &~ (1<<i), w.substr(W[i].size()) );
return memo3[key] = cnt;
}
};
// 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> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
int verify_case(const long long &Expected, const long long &Received) { if (Expected == Received) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } return 0;}
template<int N> struct Case_ { Case_(){start_time=clock();} };
char Test_(...);
int Test_(Case_<0>) {
string words_[] = {"a","ba"};
vector <string> words(words_, words_+sizeof(words_)/sizeof(*words_));
long long RetVal = 2LL;
return verify_case(RetVal, PalindromePhrases().getAmount(words)); }
int Test_(Case_<1>) {
string words_[] = {"ab","bcd","efg"};
vector <string> words(words_, words_+sizeof(words_)/sizeof(*words_));
long long RetVal = 0LL;
return verify_case(RetVal, PalindromePhrases().getAmount(words)); }
int Test_(Case_<2>) {
string words_[] = {"a", "bba", "abb"};
vector <string> words(words_, words_+sizeof(words_)/sizeof(*words_));
long long RetVal = 7LL;
return verify_case(RetVal, PalindromePhrases().getAmount(words)); }
int Test_(Case_<3>) {
string words_[] = {"aabccc", "ccbbca", "a", "acaabb", "aaa", "aab", "c", "babb", "aacaa", "b"};
vector <string> words(words_, words_+sizeof(words_)/sizeof(*words_));
long long RetVal = 47LL;
return verify_case(RetVal, PalindromePhrases().getAmount(words)); }
int Test_(Case_<4>) {
string words_[] = {"a", "aa", "aaa"};
vector <string> words(words_, words_+sizeof(words_)/sizeof(*words_));
long long RetVal = 47LL;
return verify_case(RetVal, PalindromePhrases().getAmount(words)); }
template<int N> void Run_() { cerr << "Test Case #" << N << "..." << flush; Test_(Case_<N>()); Run_<sizeof(Test_(Case_<N+1>()))==1 ? -1 : N+1>(); }
template<> void Run_<-1>() {}
int main() { Run_<0>(); }
// END CUT HERE