容易发现有了交换相邻字符的操作后，只要字符串所含有的字符种类和数量相同其就是等价的。这样的状态只有n^3级别，将其抽象成点子串变换抽象成边后就是求最长路径了，缩点dp解决。
码量巨大，不是很明白要怎样才能用3k写完。
#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<vector>
using namespace std;
int read()
{
int x=,f=;char c=getchar();
while (c<''||c>'') {if (c=='-') f=-;c=getchar();}
while (c>=''&&c<='') x=(x<<)+(x<<)+(c^),c=getchar();
return x*f;
}
#define N 55
#define P 100000000000000000LL
unsigned long long C[N][N];
int n,m,p[N*N*N],t=,tmp[];
int dfn[N*N*N],low[N*N*N],stk[N*N*N],SET[N*N*N],top=,cnt=;
bool flag[N*N*N];
char s[N],s2[N];
vector<int> ele[N*N*N];
struct magic{int n,a,b,c,x,y,z;}a[N<<];
struct data{int to,nxt;}edge[N*N*N*N];
struct biginteger
{
unsigned long long x,y;
bool operator <(const biginteger&a) const
{
return x==a.x?y<a.y:x<a.x;
}
bool operator >(const biginteger&a) const
{
return x==a.x?y>a.y:x>a.x;
}
biginteger operator +(const biginteger&a) const
{
biginteger v=(biginteger){x,y};
v.x+=a.x;v.y+=a.y;
if (v.y>=P) v.x++,v.y-=P;
return v;
}
biginteger operator *(const unsigned long long&a) const
{
unsigned long long v[]={};int n=;
biginteger tmp=(biginteger){x,y};
while (tmp.y) v[++n]=tmp.y%,tmp.y/=;
if (tmp.x)
{
n=;
while (tmp.x) v[++n]=tmp.x%,tmp.x/=;
}
for (int i=;i<=n;i++) v[i]=v[i]*a;
for (int i=;i<=n;i++)
v[i+]+=v[i]/,v[i]%=;
while (v[n+]) n++,v[n+]+=v[n]/,v[n]%=;
for (int i=;i>=;i--) tmp.y=tmp.y*+v[i];
for (int i=n;i>=;i--) tmp.x=tmp.x*+v[i];
return tmp;
}
}value[N*N*N],V[N*N*N],f[N*N*N];
int trans(int x,int y,int z){return x*(n+)*(n+)+y*(n+)+z+;}
void addedge(int x,int y){t++;edge[t].to=y,edge[t].nxt=p[x],p[x]=t;}
void tarjan(int k)
{
dfn[k]=low[k]=++cnt;
flag[k]=;stk[++top]=k;
for (int i=p[k];i;i=edge[i].nxt)
if (!dfn[edge[i].to]) tarjan(edge[i].to),low[k]=min(low[k],low[edge[i].to]);
else if (flag[edge[i].to]) low[k]=min(low[k],dfn[edge[i].to]);
if (dfn[k]==low[k])
{
t++;
while (stk[top]!=k)
{
SET[stk[top]]=t;
ele[t].push_back(stk[top]);
V[t]=V[t]+value[stk[top]];
flag[stk[top]]=;
top--;
}
SET[k]=t;ele[t].push_back(k);V[t]=V[t]+value[k];flag[k]=;top--;
}
}
namespace newgraph
{
int n,t=,p[N*N*N]={},degree[N*N*N],q[N*N*N];
struct data{int to,nxt;}edge[N*N*N*N];
void addedge(int x,int y){t++;edge[t].to=y,edge[t].nxt=p[x],p[x]=t;}
void topsort()
{
int head=,tail=;for (int i=;i<=n;i++) if (!degree[i]) q[++tail]=i;
while (tail<n)
{
int x=q[++head];
for (int i=p[x];i;i=edge[i].nxt)
{
degree[edge[i].to]--;
if (!degree[edge[i].to]) q[++tail]=edge[i].to;
}
}
}
void solve()
{
topsort();
for (int i=n;i>=;i--)
{
for (int j=p[q[i]];j;j=edge[j].nxt)
f[q[i]]=max(f[q[i]],f[edge[j].to]);
f[q[i]]=f[q[i]]+V[q[i]];
}
}
}
void rebuild()
{
memset(flag,,sizeof(flag));
for (int i=;i<=t;i++)
{
for (int j=;j<ele[i].size();j++)
for (int k=p[ele[i][j]];k;k=edge[k].nxt)
if (!flag[edge[k].to]&&SET[edge[k].to]!=i)
{
flag[edge[k].to]=;
newgraph::addedge(i,SET[edge[k].to]);
newgraph::degree[SET[edge[k].to]]++;
}
for (int j=;j<ele[i].size();j++)
for (int k=p[ele[i][j]];k;k=edge[k].nxt)
flag[edge[k].to]=;
}
newgraph::n=t;
}
int main()
{
n=read(),m=read();
for (int i=;i<=m;i++)
{
scanf("%s",s+);scanf("%s",s2+);
a[i].n=strlen(s+);
for (int j=;j<=a[i].n;j++)
if (s[j]=='A') a[i].a++;
else if (s[j]=='B') a[i].b++;
else if (s[j]=='C') a[i].c++;
for (int j=;j<=a[i].n;j++)
if (s2[j]=='A') a[i].x++;
else if (s2[j]=='B') a[i].y++;
else if (s2[j]=='C') a[i].z++;
if (a[i].a==a[i].x&&a[i].b==a[i].y&&a[i].c==a[i].z) a[i].a=a[i].b=a[i].c=n+;
}
C[][]=;
for (int i=;i<=n;i++)
{
C[i][]=C[i][i]=;
for (int j=;j<i;j++)
C[i][j]=C[i-][j-]+C[i-][j];
}
for (int i=;i<=n;i++)
for (int j=;j<=n-i;j++)
for (int k=;k<=n-i-j;k++)
{
value[trans(i,j,k)]=(biginteger){,C[n][i]};
value[trans(i,j,k)]=value[trans(i,j,k)]*C[n-i][j];
value[trans(i,j,k)]=value[trans(i,j,k)]*C[n-i-j][k];
for (int x=;x<=m;x++)
if (i>=a[x].a&&j>=a[x].b&&k>=a[x].c&&n-i-j-k>=a[x].n-a[x].a-a[x].b-a[x].c)
addedge(trans(i,j,k),trans(i-a[x].a+a[x].x,j-a[x].b+a[x].y,k-a[x].c+a[x].z));
}
t=;
for (int i=;i<=n;i++)
for (int j=;j<=n-i;j++)
for (int k=;k<=n-i-j;k++)
if (!dfn[trans(i,j,k)]) tarjan(trans(i,j,k));
rebuild();
newgraph::solve();
biginteger ans=(biginteger){,};
for (int i=;i<=t;i++) ans=max(ans,f[i]);
if (ans.x)
{
cout<<ans.x;
int x=;
while (ans.y) tmp[++x]=ans.y%,ans.y/=;
for (int i=;i>=;i--) cout<<tmp[i];
}
else cout<<ans.y;
return ;
}