#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define INIT std::ios::sync_with_stdio(false);std::cin.tie(0); #define VAR(type, ...)type __VA_ARGS__;Scan(__VA_ARGS__); template void Scan(T& t) { std::cin >> t; } templatevoid Scan(First& first, Rest&...rest) { std::cin >> first; Scan(rest...); } #define OUT(d) std::cout< c(n);for(auto& i:c)std::cin>>i; #define MAT(type, c, m, n) std::vector> c(m, std::vector(n));for(auto& r:c)for(auto& i:r)std::cin>>i; #define ALL(a) (a).begin(),(a).end() #define FOR(i, a, b) for(int i=(a);i<(b);++i) #define RFOR(i, a, b) for(int i=(b)-1;i>=(a);--i) #define REP(i, n) for(int i=0;i=0;--i) #define FORLL(i, a, b) for(ll i=ll(a);i=ll(a);--i) #define REPLL(i, n) for(ll i=0;i=0;--i) #define PAIR std::pair #define PAIRLL std::pair #define IN(a, x, b) (a<=x && x(end-start).count();std::cerr<<"[Time:"< tmp(a);std::cout << #a << "\t:";for(int i=0; i(a.size()); ++i){std::cout << tmp.front() << "\n";tmp.pop();}std::cout << "\n";} #define CHMAX(a, b) a = (((a)<(b)) ? (b) : (a)) #define CHMIN(a, b) a = (((a)>(b)) ? (b) : (a)) #define EXCEPTION(msg) throw std::string("Exception : " msg " [ in ") + __func__ + " : " + std::to_string(__LINE__) + " lines ]" #define TRY(cond, msg) try {if (cond) EXCEPTION(msg);}catch (std::string s) {std::cerr << s << std::endl;} //#define int ll using ll = long long; using ull = unsigned long long; constexpr int INFINT = 1 << 30; constexpr ll INFLL = 1LL << 60; constexpr double EPS = 0.0000000001; constexpr int MOD = 1000000007; constexpr double PI = 3.141592653589793238; double bisectionDouble(double low, double high, int repeat, std::function check) { for (int i = 0; i < repeat; ++i) { double mid = (low + high) / 2; if (check(mid)) low = mid; else high = mid; } return low; } signed main() { INIT; VAR(int, k); FOUT(10, bisectionDouble(0, 1000000000, 100, [k](double x) { // dp[i] = 現在の和がiのときのサイコロを振る残りの回数の期待値 std::vector dp(k + 1, 0); FOR(i, 1, k + 1) { FOR(j, 1, 6 + 1) { if (i > j) dp[i] += dp[i - j] / 6.0; if (j > i) dp[i] += x / 6.0; } ++dp[i]; } return dp[k] >= x; }))BR; return 0; }