1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <algorithm>
 5 #include <cmath>
 6 
 7 
 8 using namespace std;
 9 
10 #define read() freopen("sw.in", "r", stdin)
11 
12 const double eps = 1e-9;
13 const int MAX = 305;
14 double p;
15 double a[MAX][MAX];
16 int id[25][25];
17 int len = 0;
18 
19 void init() {
20         memset(id, -1 ,sizeof(id));
21         for (int i = 0; i < 20; ++i) {
22                 for (int j = 0; j <= i; ++j) {
23                         id[i][j] = len++;
24                 }
25         }
26         //printf("len = %d\n", len);
27 
28 }
29 
30 void solve( int &n) {
31         int r;
32         for (int i = 0; i < n; ++i) {
33                 r = i;
34                 for (int j = i + 1; j < n; ++j) {
35                         if (fabs(a[j][i]) > fabs(a[r][i])) r = j;
36                 }
37                 if (r != i) for (int j = 0; j <= n; ++j) swap(a[r][j], a[i][j]);
38 
39                 for (int j = n; j >= i; --j) {
40                         for (int k = i + 1; k < n; ++k) {
41                                 a[k][j] -= a[k][i] / a[i][i] * a[i][j];
42                         }
43                 }
44         }
45 
46         for (int i = n - 1; i >= 0; --i) {
47                 for (int j = i + 1; j < n; ++j) {
48                         a[i][n] -= a[j][n] * a[i][j];
49                 }
50                 a[i][n] /= a[i][i];
51         }
52 
53         //for (int i = 0; i < n; ++i)
54                 printf("%.6f\n", a[0][n]);
55 }
56 int main()
57 {
58    // read();
59     init();
60     while (~scanf("%lf", &p)) {
61             memset(a, 0, sizeof(a));
62             //cout << p << endl;
63             int u, v;
64             for (int i = 0; i < 20; ++i) {
65                     for (int j = 0; j < i; ++j) {
66                             u = id[i][j];
67 
68                             a[ u ][ u ] =  1;
69                             a[ u ][ len ] = 1;
70                             v = id[i][ max(0, j - 2)];
71                             a[u][v] -= (1.0 - p);
72                              v = id[i][j + 1];
73                             a[ u ][ v ] -= p;
74 
75 
76                     }
77                     u = id[i][i];
78                     a[ u ][ u ] = 1;
79                     a[ u ][len] = 1;
80                     v = id[i][ max(0, i - 2) ];
81                     a[ u ][ v ] -= 1 - p;
82                     v = id[i + 1][ i ];
83                     a[ u] [v ] -= p;
84 
85             }
86 
87             solve( len);
88 
89 
90     }
91     //cout << "Hello world!" << endl;
92     return 0;
93 }