#include using namespace std; #define incII(i, l, r) for(decay_t i = (l) ; i <= (r); i++) #define incIX(i, l, r) for(decay_t i = (l) ; i < (r); i++) #define incXI(i, l, r) for(decay_t i = (l) + 1; i <= (r); i++) #define incXX(i, l, r) for(decay_t i = (l) + 1; i < (r); i++) #define decII(i, l, r) for(decay_t i = (r) ; i >= (l); i--) #define decIX(i, l, r) for(decay_t i = (r) - 1; i >= (l); i--) #define decXI(i, l, r) for(decay_t i = (r) ; i > (l); i--) #define decXX(i, l, r) for(decay_t i = (r) - 1; i > (l); i--) #define inc(i, n) incIX(i, 0, n) #define dec(i, n) decIX(i, 0, n) #define inc1(i, n) incII(i, 1, n) #define dec1(i, n) decII(i, 1, n) auto inII = [](auto a, auto l, auto r) -> bool { return (l <= a && a <= r); }; auto inIX = [](auto a, auto l, auto r) -> bool { return (l <= a && a < r); }; auto inXI = [](auto a, auto l, auto r) -> bool { return (l < a && a <= r); }; auto inXX = [](auto a, auto l, auto r) -> bool { return (l < a && a < r); }; auto setmin = [](auto & a, auto b) -> bool { return (b < a ? a = b, true : false); }; auto setmax = [](auto & a, auto b) -> bool { return (b > a ? a = b, true : false); }; auto setmineq = [](auto & a, auto b) -> bool { return (b <= a ? a = b, true : false); }; auto setmaxeq = [](auto & a, auto b) -> bool { return (b >= a ? a = b, true : false); }; using LL = long long int; using LD = long double; #define PB push_back #define EB emplace_back #define MP make_pair #define MT make_tuple #define FI first #define SE second #define FR front() #define BA back() #define ALL(a) begin(a), end(a) #define RALL(a) rbegin(a), rend(a) #define RV(a) reverse(ALL(a)) #define ST(a) sort(ALL(a)) #define RST(a) sort(RALL(a)) #define SC static_cast #define SI(a) SC(a.size()) #define SL(a) SC(a.size()) #define RF(e, ...) for(auto && e: __VA_ARGS__) #define SF(a, ...) for(auto && [__VA_ARGS__]: a) #define until(...) while(not(__VA_ARGS__)) #define if_not(...) if(not(__VA_ARGS__)) #define ef else if #define UR assert(false) // output valarray template ostream & operator<<(ostream & os, valarray const & a) { inc(i, SI(a)) { os << (i == 0 ? "" : " ") << a[i]; } return os; } template istream & operator>>(istream & is, vector & v); template ostream & operator<<(ostream & os, vector const & v); template istream & operator>>(istream & is, array & a); template ostream & operator<<(ostream & os, array const & a); template istream & operator>>(istream & is, pair & p); template ostream & operator<<(ostream & os, pair const & p); template istream & operator>>(istream & is, tuple & t); template ostream & operator<<(ostream & os, tuple const & t); template void tin_ (istream & is, T & t) { if constexpr(I < tuple_size::value) { is >> get(t); tin_(is, t); } } template void tout_(ostream & os, T const & t) { if constexpr(I < tuple_size::value) { if(I != 0) { os << " "; } os << get(t); tout_(os, t); } } template istream & operator>>(istream & is, vector & v) { for(auto && e: v) { is >> e; } return is; } template ostream & operator<<(ostream & os, vector const & v) { string ss; for(auto && e: v) { os << ss << e; ss = " "; } return os; } template istream & operator>>(istream & is, array & a) { for(auto && e: a) { is >> e; } return is; } template ostream & operator<<(ostream & os, array const & a) { string ss; for(auto && e: a) { os << ss << e; ss = " "; } return os; } template istream & operator>>(istream & is, pair & p) { return is >> p.first >> p.second; } template ostream & operator<<(ostream & os, pair const & p) { return os << p.first << " " << p.second; } template istream & operator>>(istream & is, tuple & t) { tin_ (is, t); return is; } template ostream & operator<<(ostream & os, tuple const & t) { tout_(os, t); return os; } auto * IS = & cin; auto * OS = & cout; template void in(A & ... a) { (* IS >> ... >> a); } #define IN(...) __VA_ARGS__; in(__VA_ARGS__) template auto make_v(A a) { return a; } template auto make_v(A a, int n, M ... m) { return vector(n, make_v(a, m ...)); } template auto read_v(N ... n) { auto a = make_v(A { }, n ...); in(a); return a; } void out_([[maybe_unused]] string const & s) { } template void out_([[maybe_unused]] string const & s, A const & a) { * OS << a; } template void out_( string const & s, A const & a, B const & ... b) { * OS << a << s; out_(s, b ...); } auto outF = [](string const & s, string const & t, auto const & ... a) { out_(s, a ...); * OS << t << flush; }; auto outN = [](auto const & ... a) { outF("" , "" , a ...); }; auto outS = [](auto const & ... a) { outF(" " , " " , a ...); }; auto outL = [](auto const & ... a) { outF("\n", "\n", a ...); }; auto outSN = [](auto const & ... a) { outF(" " , "" , a ...); }; auto outNL = [](auto const & ... a) { outF("" , "\n", a ...); }; auto outSL = [](auto const & ... a) { outF(" " , "\n", a ...); }; auto out = outSL; template void disp_(A const & a) { * OS << a; } template void disp_(A const & a, string const & s, T const & ... t) { string ss; for(auto && e: a) { * OS << ss; ss = s; disp_(e, t ...); } } auto dispI = [](auto const & a, auto const & s, auto const & ... t) { disp_(a, t ...); * OS << s << flush; }; auto dispT = [](auto const & a, auto const & s, auto const & ... t) { for(auto && e: a) { disp_(e, t ...); * OS << s; } * OS << flush; }; auto dispL = [](auto const & a, auto const & ... t) { dispT(a, "\n", t ...); }; struct OS_init { OS_init() { * OS << boolalpha << fixed << setprecision(20); } } os_init_; // ---- ---- #define A { x[0], x[1], x[2], n } int main() { using I = valarray; using D = valarray; auto toD = [](I x) -> D { D y(SI(x)); inc(i, SI(x)) { y[i] = x[i]; } return y; }; map, D> memo; function f = [&](I x, int n) -> D { D ans(3); if(n == 0 || x.sum() == 3) { return ans; } if(memo.count(A) == 1) { return memo[A]; } double s = x.sum() * (x.sum() - 1); D p = toD(x * (x - 1)) / s; inc(i, 3) { if(x[i] == 1) { continue; } I one(3); one[i] = 1; ans += p[i] * (toD(one) + f(x - one, n - 1)); } ans += (1 - p.sum()) * f(x, n - 1); return memo[A] = ans; }; int IN(a, b, c, n); cout.precision(12); out(f({ a, b, c }, n)); }