AA=0,AB=1,BA=2,BB=3
cnt[0]=no. of AA,cnt[1]=no. of AB...........

int sz=2;
if(last letter==A) szvalue=0;
if(last letter==B) szvalue=2;

define DP[cnt[0]+2][cnt[1]+2][cnt[2]+2][cnt[3]+2][sz];

dp 1,0,0,0,0=1; //for AA
dp 0,1,0,0,1=1; //for AB