#include using namespace std; typedef long long signed int LL; typedef long long unsigned int LU; #define incID(i, l, r) for(int i = (l) ; i < (r); i++) #define incII(i, l, r) for(int i = (l) ; i <= (r); i++) #define decID(i, l, r) for(int i = (r) - 1; i >= (l); i--) #define decII(i, l, r) for(int i = (r) ; i >= (l); i--) #define inc(i, n) incID(i, 0, n) #define inc1(i, n) incII(i, 1, n) #define dec(i, n) decID(i, 0, n) #define dec1(i, n) decII(i, 1, n) #define inII(v, l, r) ((l) <= (v) && (v) <= (r)) #define inID(v, l, r) ((l) <= (v) && (v) < (r)) #define PB push_back #define EB emplace_back #define MP make_pair #define FI first #define SE second #define UB upper_bound #define LB lower_bound #define PQ priority_queue #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() #define FOR(it, v) for(auto it = v.begin(); it != v.end(); ++it) #define RFOR(it, v) for(auto it = v.rbegin(); it != v.rend(); ++it) template bool setmin(T & a, T b) { if(b < a) { a = b; return true; } else { return false; } } template bool setmax(T & a, T b) { if(b > a) { a = b; return true; } else { return false; } } template bool setmineq(T & a, T b) { if(b <= a) { a = b; return true; } else { return false; } } template bool setmaxeq(T & a, T b) { if(b >= a) { a = b; return true; } else { return false; } } template T gcd(T a, T b) { return (b == 0 ? a : gcd(b, a % b)); } template T lcm(T a, T b) { return a / gcd(a, b) * b; } // ---- ---- int d[26][13] = { { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 2300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 12650, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 53118, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 176860, 240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 478420, 2280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 1067895, 13680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 1984881, 58048, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 3083468, 184536, 756, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 3998100, 453480, 5820, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 4297872, 874664, 27716, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 3780704, 1328328, 90492, 776, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, { 2664548, 1575736, 211572, 5536, 8, 0, 0, 0, 0, 0, 0, 0, 0 }, { 1456572, 1430612, 358504, 22836, 236, 0, 0, 0, 0, 0, 0, 0, 0 }, { 587935, 958328, 435028, 59608, 2068, 8, 0, 0, 0, 0, 0, 0, 0 }, { 162362, 445644, 363960, 100544, 8883, 180, 2, 0, 0, 0, 0, 0, 0 }, { 27088, 129888, 194820, 106288, 21256, 1336, 24, 0, 0, 0, 0, 0, 0 }, { 2176, 19788, 57992, 64292, 28016, 4612, 220, 4, 0, 0, 0, 0, 0 }, { 48, 1064, 7296, 18136, 18106, 7368, 1064, 48, 0, 0, 0, 0, 0 }, { 0, 0, 186, 1498, 4148, 4528, 1998, 282, 10, 0, 0, 0, 0 }, { 0, 0, 0, 0, 128, 600, 932, 544, 96, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 24, 108, 132, 36, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 16, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 }, }; double comb_v[100][100]; void init() { inc(i, 100) { inc(j, 100) { comb_v[i][j] = (j == 0 ? 1 : (i == 0 ? 0 : comb_v[i - 1][j] + comb_v[i - 1][j - 1])); } } } double comb(int a, int b) { return (inII(b, 0, a) ? comb_v[a][b] : 0); } int main() { int n; cin >> n; init(); double ans = 0.0; incII(i, 0, min(n, 25)) { double a = 0.0, b = 0.0; incII(j, 0, 12) { a += d[i][j] * j; b += d[i][j]; } ans += comb(25, i) * comb(99 - 25, n - i) * a / b; } printf("%.8f\n", ans / comb(99, n)); //printf("%.8f %.8f\n", ans, comb(99, n)); /* inc(i, 20) { inc(j, 20) { printf("%.0f ", comb_v[i][j]); } cout << endl; } cout << endl; */ return 0; } // ---- int c[26][13]; int f(int i, int j) { return (i * 5 + j); } int b(int bit, int p) { return (bit >> p) % 2; } int bc(int v) { int s = 0; while(v) { s += v % 2; v /= 2; } return s; } int main2() { inc(bit, 1 << 25) { int v = 0, s; inc(i, 5) { s = 0; inc(j, 5) { s += b(bit, f(i, j)); } if(s == 5) { v++; } } inc(j, 5) { s = 0; inc(i, 5) { s += b(bit, f(i, j)); } if(s == 5) { v++; } } s = 0; inc(i, 5) { s += b(bit, f(i, i)); } if(s == 5) { v++; } s = 0; inc(i, 5) { s += b(bit, f(i, 4 - i)); } if(s == 5) { v++; } c[bc(bit)][v]++; } inc(i, 26) { cout << "\t{ "; inc(j, 13) { cout << (j == 0 ? "" : ", ") << c[i][j]; } cout << " }, " << endl; } return 0; }