1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <cmath>
 5 using namespace std;
 6 
 7 double p,A[235][235];
 8 int cnt;
 9 struct node
10 {
11     int i,j;
12     node(int i=0,int j=0):i(i),j(j){}
13 }map[235];
14 const double eps=1e-8;
15 int dcmp(double x)
16 {
17     if(fabs(x)<eps) return 0;
18     if(x-0>eps) return 1;
19     return -1;
20 }
21 void swap(int &a,int &b){int t=a;a=b;b=t;}
22 inline int max(int a,int b){return a>b?a:b;}
23 inline int min(int a,int b){return a<b?a:b;}
24 void init()
25 {
26     cnt=0;
27     for(int i=0;i<=20;i++)
28     for(int j=i;j<=20;j++)
29         map[cnt++]=node(i,j);
30 }
31 int find(int x,int y)
32 {
33     int c=0;
34     for(int i=0;i<=20;i++)
35     for(int j=i;j<=20;j++)
36     {
37         if(i==x&&j==y)
38             return c;
39         c++;
40     }
41 }
42 void build_matrix()
43 {
44     memset(A,0,sizeof(A));
45     for(int i=0;i<cnt;i++)
46     {
47         A[i][i]=1;
48         if(map[i].j==20){A[i][cnt]=0;continue;}
49         int x=min(map[i].i+1,20),y=map[i].j;
50         if(x>y) swap(x,y);
51         int pos=find(x,y);
52         A[i][pos]-=p;
53         x=max(map[i].i-2,0);y=map[i].j;
54         pos=find(x,y);
55         A[i][pos]-=1-p;
56         A[i][cnt]+=1;
57     }
58 }
59 void gauss(int n)
60 {
61     int i,j,k,r;
62     for(i=0;i<n;i++)
63     {
64         r=i;
65         for(j=i+1;j<n;j++)
66             if(fabs(A[j][i])>fabs(A[r][i])) r=j;
67         if(dcmp(A[r][i])==0) continue;
68         if(r!=i) for(j=0;j<=n;j++) swap(A[r][j],A[i][j]);
69         for(k=0;k<n;k++) if(k!=i)
70             for(j=n;j>=i;j--) A[k][j]-=A[k][i]/A[i][i]*A[i][j];
71     }
72     for(i=n-1;i>=0;i--)
73     {
74          for(j=i+1;j<cnt;j++)
75             A[i][cnt]-=A[j][cnt]*A[i][j];
76          A[i][cnt]/=A[i][i];
77     }
78 }
79 int main()
80 {
81     init();
82     while(~scanf("%lf",&p))
83     {
84         build_matrix();
85         gauss(cnt);
86         printf("%.6lf\n",A[0][cnt]);
87     }
88     return 0;
89 }