#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<double> CMP;
static const unsigned MODVAL = 1000000009;
struct mint
{
unsigned val;
mint():val(0){}
mint(int x):val(x%MODVAL) {}
mint(unsigned x):val(x%MODVAL) {}
mint(LL x):val(x%MODVAL) {}
};
mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
mint operator+(mint x, mint y) { return x+=y; }
mint operator-(mint x, mint y) { return x-=y; }
mint operator*(mint x, mint y) { return x*=y; }
mint POW(mint x, LL e) { mint v=1; for(;e;x*=x,e>>=1) if(e&1) v*=x; return v; }
mint& operator/=(mint& x, mint y) { return x *= POW(y, MODVAL-2); }
mint operator/(mint x, mint y) { return x/=y; }
vector<mint> FAC_(1,1);
mint FAC(LL n) { while( FAC_.size()<=n ) FAC_.push_back( FAC_.back()*FAC_.size() ); return FAC_[n]; }
mint P(LL n, LL k) {
return k<0 || n<k ? 0 : FAC(n) / FAC(n-k);
}
// Tested: SRM 468 Lv2
template<typename T>
struct DP3x
{
int N1, N2, N3;
vector<T> data;
DP3x(int, int N2, int N3, const T& t = T())
: N1(2), N2(N2), N3(N3), data(N1*N2*N3, t) { assert(data.size()*sizeof(T) < (1<<26)); }
T& operator()(int i1, int i2, int i3)
{ i1&=1; return data[ ((i1*N2)+i2)*N3+i3 ]; }
void swap(DP3x& rhs)
{ data.swap(rhs.data); }
};
template<typename T>
struct DP3
{
int N1, N2, N3;
vector<T> data;
DP3(int N1, int N2, int N3, const T& t = T())
: N1(N1), N2(N2), N3(N3), data(N1*N2*N3, t) { assert(data.size()*sizeof(T)<(1<<26)); }
T& operator()(int i1, int i2, int i3)
{ return data[ ((i1*N2)+i2)*N3+i3 ]; }
void swap(DP3& rhs)
{ data.swap(rhs.data); }
};
class ColorfulBuilding { public:
int count(vector <string> color1, vector <string> color2, int L)
{
string C1 = accumulate(color1.begin(), color1.end(), string());
string C2 = accumulate(color2.begin(), color2.end(), string());
int N = C1.size();
vector<int> C;
for(int i=0; i<N; ++i)
C.push_back(to_i(C1[i])*52 + to_i(C2[i]));
return solve(C, L).val;
}
static int to_i(char c)
{
return ('A'<=c && c<='Z' ? c-'A' : c-'a'+26);
}
mint solve(vector<int>& C, int L)
{
int N = C.size();
DP3x<mint> dp(L+1, N, N+1);
for(int c=1; c<=L; ++c)
{
for(int x=0; x<N; ++x)
{
dp(c,x,1) = (c==1 ? 1 : 0);
for(int i=2; i<=x+1; ++i)
{
mint sum = 0;
for(int y=0; y<x; ++y) {
int cc = (C[x]==C[y] ? c : c-1);
for(int k=1; k<=y+1 && k<=i-1; ++k)
sum += dp(cc,y,k) * P(y+1-k, i-1-k);
}
dp(c,x,i) = sum;
}
}
}
mint ans = 0;
for(int i=1; i<=N; ++i)
ans += dp(L, N-1, i) * P(N-i, N-i);
return ans;
}
};
// 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(_, ColorfulBuilding().count(color1, color2, L));}
int main(){
CASE(0)
string color1_[] = {"aaba"};
vector <string> color1(color1_, color1_+sizeof(color1_)/sizeof(*color1_));
string color2_[] = {"aaaa"};
vector <string> color2(color2_, color2_+sizeof(color2_)/sizeof(*color2_));
int L = 3;
int _ = 6;
END
CASE(1)
string color1_[] = {"aaba"};
vector <string> color1(color1_, color1_+sizeof(color1_)/sizeof(*color1_));
string color2_[] = {"aaba"};
vector <string> color2(color2_, color2_+sizeof(color2_)/sizeof(*color2_));
int L = 4;
int _ = 0;
END
CASE(2)
string color1_[] = {"ab", "ba", "a", "aab"};
vector <string> color1(color1_, color1_+sizeof(color1_)/sizeof(*color1_));
string color2_[] = {"bb", "ba", "a", "aba"};
vector <string> color2(color2_, color2_+sizeof(color2_)/sizeof(*color2_));
int L = 5;
int _ = 432;
END
CASE(3)
string color1_[] = {"xxxxxxxxxxxxxxxxxxxx",
"xxxxxxxxxxxxxxxxxxxx",
"xxOOOOOOOOOOOOOOOOxx",
"xxOOOOOOOOOOOOOOOOxx",
"xxOOxxxxxxxxxxxxxxxx",
"xxOOxxxxxxxxxxxxxxxx",
"xxOOxxxxxxxxxxxxxxxx",
"xxOOxxxxxxxxxxxxxxxx",
"xxOOxxxxxxxxxxxxxxxx",
"xxOOxxxxxxxxxxxxxxxx",
"xxOOxxxxxxxxxxxxxxxx",
"xxOOOOOOOOOOOOOOOOxx",
"xxOOOOOOOOOOOOOOOOxx",
"xxxxxxxxxxxxxxxxOOxx",
"xxxxxxxxxxxxxxxxOOxx",
"xxxxxxxxxxxxxxxxOOxx",
"xxxxxxxxxxxxxxxxOOxx",
"xxxxxxxxxxxxxxxxOOxx",
"xxxxxxxxxxxxxxxxOOxx",
"xxxxxxxxxxxxxxxxOOxx",
"xxOOOOOOOOOOOOOOOOxx",
"xxOOOOOOOOOOOOOOOOxx",
"xxxxxxxxxxxxxxxxxxxx",
"xxxxxxxxxxxxxxxxxxxx"};
vector <string> color1(color1_, color1_+sizeof(color1_)/sizeof(*color1_));
string color2_[] = {"xxxxxxxxxxxxxxxxxxxx",
"xxxxxxxxxxxxxxxxxxxx",
"xxOOOOOOOOOOOOOOOOxx",
"xxOOOOOOOOOOOOOOOOxx",
"xxOOxxxxxxxxxxxxOOxx",
"xxOOxxxxxxxxxxxxOOxx",
"xxOOxxxxxxxxxxxxOOxx",
"xxOOxxxxxxxxxxxxOOxx",
"xxOOxxxxxxxxxxxxOOxx",
"xxOOxxxxxxxxxxxxOOxx",
"xxOOxxxxxxxxxxxxOOxx",
"xxOOOOOOOOOOOOOOOOxx",
"xxOOOOOOOOOOOOOOOOxx",
"xxOOxxxxxxxxxxxxOOxx",
"xxOOxxxxxxxxxxxxOOxx",
"xxOOxxxxxxxxxxxxOOxx",
"xxOOxxxxxxxxxxxxOOxx",
"xxOOxxxxxxxxxxxxOOxx",
"xxOOxxxxxxxxxxxxOOxx",
"xxOOxxxxxxxxxxxxOOxx",
"xxOOOOOOOOOOOOOOOOxx",
"xxOOOOOOOOOOOOOOOOxx",
"xxxxxxxxxxxxxxxxxxxx",
"xxxxxxxxxxxxxxxxxxxx"};
vector <string> color2(color2_, color2_+sizeof(color2_)/sizeof(*color2_));
int L = 58;
int _ = 619787617;
END
CASE(4)
string color1_[] = {"SJXcabKTWeUXhwxGixFepQaQlFxrAedNAtVP",
"gorBIkcTlOFbLDbFeElYAyAqszQdMbpxSRdE",
"SQVHPehlNtesbJDflyGxMqvgzjXisRnqDcQO",
"pIAEBwbmpPWCooQAujbGXFGLvXxTmExLARkf",
"AFnWyWKVObfxDGCjTxdZaObgwdxlPKtIxaAd",
"uznMpJVNjAofbHJjOrZeSHgSagOCUMGbvkVR",
"LBRrDbTAyKfVnedKiRfzgRzECpcsziqaTwdo",
"JrJHvsEVVGDkNVGqLbpxyLDPloBuNDQKnReI",
"SSYpbjKHSCnQhuyYrVauWDHDyhAoGyecrZMv",
"UdetQfWEUWHHuAxRSdkJOOJSixKpQXpCFZHO",
"KXVsQbuQtIgsULOMsTvPFNUqkBldMTLCipYK",
"hoXConjnDWQkZVtyZlwSedvdVrNWqQhGUClQ",
"TpsvvyoXsXmQpBAGGVDrXCkodoRHQZmpoQDW",
"csiJspzTqeFBRmPgeEtTAzfrfCGlTZqcPuyO",
"vsPDVBJVaJmUAtDdcsKoUkPEbDmAwtZKwjjP",
"MOfoMhMiKIvGQoeIJXHzyClWRtRuKXMqxUAF",
"KyyUCkRBjsYvmPFFEGBqqVhIUdtvIyyLacfu",
"BfuwfSajSlcuTzhMufHSQLudvGEGlyHsEmBD",
"PLpIXZkdyXveTMfSvqnDGKWOZrTBMUIlZrqF",
"dzVMCqrSLbanRJTYpDJNHAOLPSzmvSEPQJYm",
"rAjRkrSjouJyFaCSPPLYSzqDmMoADyWAbobJ",
"eOCBrJNoyFnGpXpxiExXcoOHnVsaEPXhPfLe",
"XMjRksnxWssPEINhdhbiLBSYpCLtwNshFjXS",
"HnnDeUAbuswsgsYQuAaXySLkFYUwFXwYTreM",
"uqLnwOEGbwZZDgAAWEdLRZxFlogDmlhjhgHM",
"NcfaQsgPQfirkYDRFrLQpySmBGfRHumKULZf",
"mOpmmgclsxRzXskEywfryqCRyATNoJwnlHiD",
"AnoKoKAjrasttjNlHCROnvTJMhEHlVPVoVMo",
"yegLyIuRkkENFAjwzDoPLKjgUHHEkfzYDIpo",
"EcxRGGfuaBXUFXkSxctJWOLmmVbvoMkWtTvV",
"nBMkOBHgaltEVzfyGxseGhmBscfGIbxFbqRn",
"GvkEcLtqdOofGtsbWDafVMbNdJxsffKDzSiR",
"jhZQUVzTzalrZcebvyqPWtOUUyniBKTWdyLi",
"ODJLQPMdjDdTlxrfGsNmBfeGYjzeXApqKDhJ",
"vlJkWMzdVQujKdLViQClOrJXMTBkuZEasFgg",
"FAsbuzrLVIgaryqXBfuBRAbReleXSSgEKSvt"};
vector <string> color1(color1_, color1_+sizeof(color1_)/sizeof(*color1_));
string color2_[] = {"XAhlUHtfjOpOlQlowWppQcodMGUiqoLobxnD",
"IDzGlKrHiVGdBjZxIcoxjwagbWieKvUwZrjg",
"SkpkTVeIFeoNQzUUgmYAYskKONNZdgXxSiWd",
"rXBGhTmqnvxkmqiutoDzPusDiOUggEFXGCzm",
"fzrxVuTbFXunGbeEavjshmrIRlDorTuISCxn",
"LsvIaxTkOBjcskiekmrKNNFEXqnfMNXLWqqu",
"ekzxGIlbJPVEQPYAbTuMtZKsCiubDXDiBVzU",
"hZuOCJxvBOYENGSFcUiKKAKfCdebutVmnyvB",
"UveNkKRQmHnedrROQOpHJfrHjwcNLUShlDbn",
"ptUkvbaGDryHRkYfHKLkSgVpjWCEcgazyxGK",
"nVPYEqTTJsRPjzjfdOiULhnZPFeNcnbXaQlk",
"IPXBXRhMQIkxpygsgbcRfMuvIcuzUPPHGOWX",
"yWWlNyEyqZSIOXBFAybIuFpVqpvmKRaRFrAE",
"EvBJVtHvKhjrFcmtpdBbFTdTVtXXZQKAglKT",
"bCVjHzUvyINFkxXageZQMzCyNhcifACdJVDh",
"lZITYcDSeIbLweyFtoMAfOQyBNupKlhcNpgo",
"BduslNrJdWOUukYFFidEkMFaghfofpxVgvJd",
"YrJpDZKqdjEPzdLsOQEdkcrBfNHPemXHokCW",
"GjeUKSGjDlgKTyUGNrMQbBLxRUcgrWpkAwOD",
"wgxTcswqdJHaDugNIRMvrhBsdDaJAssVbSRW",
"qmVmqFEpvgGioMXDSFqEoQcDOAaUoGPEovSO",
"KrukPlpfOhawaovCfteTSCIdLMrtImVtiMyQ",
"ykwmxHsKMFzFHwcbyyedLvhZPnaNGqJMMCxd",
"HUNYCXjNLQIFCLLGpCXHBCHLTxLynBxnHFbx",
"uwjzbNbJepVFgMPUXVirxYHzExquBEtPmKju",
"xXAxAbJePyUsVHeLytDvAxBGMRtnvCEiZZqe",
"xMkQoIVxWPXPgaOYmDjTOXiMImVdzojERNxS",
"dwICFwMAmdOIUxyAdXdshasnzwyhfnVWVqZJ",
"etypXNVvSTEQvriGBZdSGmDEHhvpSqkFklCS",
"YkxpFBCRYUueRcKaJUXVdaMoYMYEooPQVMOr",
"DTrexDqclZNKdPuTRFHualJSFziCLPCZjpxo",
"TfEijcAsSJPikkmBSbXMqYHAhPTcpcKVSkIX",
"xKXHYPYMJxFpSbxltDKYuRiTkOLxpQKnXZPs",
"YFYuvuYHfpFJcrLNIdlNfBxRnWdppsdalBkx",
"NFTysBvNFjejdnlhRTclbcfGipNCxpFEOriY",
"thkgVflJYmbUYbIlafNUMGePQWiZyYzYXvUR"}
;
vector <string> color2(color2_, color2_+sizeof(color2_)/sizeof(*color2_));
int L = 1200;
int _ = 396065426;
END
/*
CASE(5)
string color1_[] = ;
vector <string> color1(color1_, color1_+sizeof(color1_)/sizeof(*color1_));
string color2_[] = ;
vector <string> color2(color2_, color2_+sizeof(color2_)/sizeof(*color2_));
int L = ;
int _ = ;
END
CASE(6)
string color1_[] = ;
vector <string> color1(color1_, color1_+sizeof(color1_)/sizeof(*color1_));
string color2_[] = ;
vector <string> color2(color2_, color2_+sizeof(color2_)/sizeof(*color2_));
int L = ;
int _ = ;
END
*/
}
// END CUT HERE