1 #include <iostream>
  2 #include <cstdio>
  3 #include <cstring>
  4 #include <queue>
  5 #include <algorithm>
  6 #include <cmath>
  7 using namespace std;
  8 
  9 const int N=250;
 10 const int SZ=26;
 11 const double eps=1e-8;
 12 double p[27],A[N][N];
 13 bool inf[N];
 14 struct AC
 15 {
 16     int ch[N][26];
 17     int sz,val[N],fail[N];
 18     void init(){
 19         sz=1;memset(val,0,sizeof(val));
 20         memset(ch[0],0,sizeof(ch[0]));
 21     }
 22     void insert(char *s)
 23     {
 24         int rt=0;
 25         for (int i=0;s[i];i++){
 26             int c=s[i]-‘a‘;
 27             if (ch[rt][c]==0){
 28                 ch[rt][c]=sz;
 29                 memset(ch[sz],0,sizeof(ch[sz]));
 30                 sz++;
 31             }
 32             rt=ch[rt][c];
 33         }
 34         val[rt]=1;
 35     }
 36     void getfail()
 37     {
 38         queue<int>q;
 39         for (int i=0;i<SZ;i++)
 40         {
 41             int c=ch[0][i];
 42             if (c){ q.push(c);fail[c]=0; }
 43         }
 44         while (!q.empty())
 45         {
 46             int u=q.front();q.pop();
 47             for (int i=0;i<SZ;i++)
 48             {
 49                 int c=ch[u][i];
 50                 if (!c){
 51                     ch[u][i]=ch[fail[u]][i];
 52                 }else 
 53                 {
 54                     int v=fail[u];
 55                     q.push(c);
 56                     fail[c]=ch[v][i];
 57                     val[c]|=val[fail[c]];
 58                 }
 59             }
 60         }
 61     }
 62 }ac;
 63 
 64 void build_matrix()
 65 {
 66     int i,j;
 67     memset(A,0,sizeof(A));
 68     for(i=0;i<ac.sz;i++)
 69     {
 70         if(ac.val[i]){A[i][i]=1;A[i][ac.sz]=0;}
 71         else
 72         {
 73             for(j=0;j<SZ;j++){int v=ac.ch[i][j];A[i][v]+=p[j];}
 74             A[i][i]+=-1;A[i][ac.sz]=-1;
 75         }
 76     }
 77 }
 78 
 79 void gauss(int n)
 80 {
 81     int i,j,k,r;
 82     for(i=0;i<n;i++)
 83     {
 84         r=i;
 85         for(j=i+1;j<n;j++)
 86             if(fabs(A[j][i])>fabs(A[r][i])) r=j;
 87             if(fabs(A[r][i])<eps) continue;
 88             if(r!=i) for(j=0;j<=n;j++) swap(A[r][j],A[i][j]);
 89             for(k=0;k<n;k++) if(k!=i)
 90                 for(j=n;j>=i;j--) A[k][j]-=A[k][i]/A[i][i]*A[i][j];
 91     }
 92     memset(inf,0,sizeof(inf));
 93     for(i=ac.sz-1;i>=0;i--){
 94         if(fabs(A[i][i])<eps&&fabs(A[i][ac.sz])>eps) inf[i]=1;
 95         for(j=i+1;j<ac.sz;j++)
 96             if(fabs(A[i][j])>eps&&inf[j]) inf[i]=1;
 97     }
 98     if(inf[0]) printf("Infinity\n");
 99     else printf("%.6lf\n",A[0][ac.sz]/A[0][0]+eps);
100 }
101 
102 int main()
103 {
104     //freopen("b.txt","w",stdout);
105     int n,i,j;char s[20];
106     while(~scanf("%d",&n))
107     {
108         ac.init();
109         for(i=0;i<SZ;i++) scanf("%lf",p+i);
110         for(i=0;i<n;i++)
111         {
112             scanf("%s",s);ac.insert(s);
113         }
114         ac.getfail();
115         build_matrix();
116         gauss(ac.sz);
117     }
118     return 0;
119 }