#include<iostream>

#include<cstdio>

#include<cstring>

#include<string>

#include<algorithm>

#include<cctype>

#include<cmath>

#include<cstdlib>

#include<queue>

#include<ctime>

#include<vector>

#include<set>

#include<map>

#include<stack>

using namespace std;

#define sp cout<<"---------------------------------------------------"<<endl;

long long dp[][];int cnt,fa[];

class PossibleOrders{

      public:

          int sf(int x){return fa[x]==x?x:fa[x]=sf(fa[x]);}

          void work(string s){

              int i,k=,x=,y=,n=s.length();

              for(i=;i<n;i++)

                if(s[i]=='=')k++;

                  else if(!k)x=(x<<)+(x<<)+(s[i]-'');

                  else y=(y<<)+(y<<)+(s[i]-'');

              if(sf(x)!=sf(y)){

                  cnt--;

                  fa[sf(x)]=sf(y);

              }

              return;

          }

          long long howMany(int num,vector<string>facts){

              int i,j,n=num;

            long long ans=;

            cnt=n;

            for(i=;i<n;i++)fa[i]=i;

            for(i=;i<facts.size();i++)work(facts[i]);

              for(i=;i<=n;i++)

              for(j=;j<=n;j++)

                dp[i][j]=;

            dp[][]=;

              for(i=;i<=cnt;i++)

              for(j=;j<=cnt;j++)

                  dp[i][j]=dp[i-][j-]*j+dp[i-][j]*j;

              for(i=;i<=cnt;i++)ans+=dp[cnt][i];

              return ans;

          }

};