// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll #define double ld #define rep(i,n) for (int i = 0; i < (int)(n); i++) #define rep1(i,n) for (int i = 1; i <= (int)(n); i++) #define repR(i,n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i,n) for (int i = (int)(n); i >= 1; i--) #define loop(i,a,B) for (int i = a; i B; i++) #define loopR(i,a,B) for (int i = a; i B; i--) #define all(x) (x).begin(), (x).end() #define allR(x) (x).rbegin(), (x).rend() #define pb push_back #define eb emplace_back #define mp make_pair #define fst first #define snd second template auto constexpr inf = numeric_limits::max()/2-1; auto constexpr INF32 = inf; auto constexpr INF64 = inf; auto constexpr INF = inf; #ifdef LOCAL #include "debug.hpp" #define dump(...) cerr << "[" << setw(3) << __LINE__ << ":" << __FUNCTION__ << "] ", dump_impl(#__VA_ARGS__, __VA_ARGS__) #define say(x) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] " << x << endl #define debug if (1) #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #endif template using pque_max = priority_queue; template using pque_min = priority_queue, greater >; template ::value>::type> ostream& operator<<(ostream& os, T const& v) { bool f = true; for (auto const& x : v) os << (f ? "" : " ") << x, f = false; return os; } template ::value>::type> istream& operator>>(istream& is, T &v) { for (auto& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << "(" << p.first << ", " << p.second << ")"; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > y) { x = y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < y) { x = y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b,e,typename iterator_traits::value_type{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(v.begin(), v.end(), x)-v.begin(); } template int ubd(C const& v, T const& x) { return upper_bound(v.begin(), v.end(), x)-v.begin(); } template int ppt(C const& v, F f) { return partition_point(v.begin(), v.end(), f)-v.begin(); } // <<< // >>> matrix template struct Matrix { int n,m; vector > a; Matrix() {} Matrix(int n, int m) : n(n), m(m), a(n) { assert(n > 0 && m > 0); rep (i,n) a[i].resize(m); } Matrix(initializer_list > init) { for (auto ls : init) { a.emplace_back(); for (auto x : ls) a.back().emplace_back(x); } n = a.size(); assert(n > 0); m = a[0].size(); assert(m > 0); } vector const& operator[](int i) const { assert(0 <= i && i < n); return a[i]; } vector & operator[](int i) { assert(0 <= i && i < n); return a[i]; } bool operator==(Matrix const& x) const { if (n != x.n || m != x.m) return false; rep (i,n) rep (j,m) if (a[i][j] != x[i][j]) return false; return true; } bool operator!=(Matrix const& x) const { return !(*this == x); } Matrix& operator+=(Matrix const& x) { assert(n == x.n && m == x.m); rep (i,n) rep (j,m) a[i][j] += x[i][j]; return *this; } Matrix& operator-=(Matrix const& x) { assert(n == x.n && m == x.m); rep (i,n) rep (j,m) a[i][j] -= x[i][j]; return *this; } Matrix operator+(Matrix const& x) const { return Matrix(*this) += x; } Matrix operator-(Matrix const& x) const { return Matrix(*this) -= x; } Matrix operator*(Matrix const& x) const { assert(m == x.n); Matrix ret(n,x.m); rep (i,n) rep (j,m) rep (k,x.m) ret[i][k] += a[i][j] * x[j][k]; return ret; } Matrix& operator*=(Matrix const& x) { auto res = (*this)*x; swap(a, res.a); return *this; } Matrix operator+() const { return *this; } Matrix operator-() const { Matrix x = *this; rep (i,n) rep (j,m) x[i][j] = -x[i][j]; return x; } Matrix& operator*=(T const& c) { rep (i,n) rep (j,m) a[i][j] *= c; return *this; } Matrix operator*(T const& c) const { return Matrix(*this) *= c; } friend Matrix operator*(T const& c, Matrix const& x) { Matrix ret = x; rep (i,x.n) rep (j,x.m) ret[i][j] = c*x[i][j]; return ret; } Matrix& operator/=(T const& c) { rep (i,n) rep (j,m) a[i][j] /= c; return *this; } Matrix operator/(T const& c) const { return Matrix(*this) /= c; } static Matrix identity(int n) { Matrix ret(n,n); rep (i,n) ret[i][i] = 1; return ret; } Matrix pow(ll k) const { assert(n == m); assert(k >= 0); Matrix v = *this, r = Matrix::identity(n); for (; k > 0; k >>= 1, v *= v) if (k&1) r *= v; return r; } friend istream& operator>>(istream& is, Matrix& x) { rep (i,x.n) rep (j,x.m) is >> x[i][j]; return is; } #ifdef LOCAL friend string to_s(Matrix const& x) { string ret; rep (i,x.n) { ret += "\n("; rep (j,x.m) ret += " " + to_s(x[i][j]); ret += " )"; } return ret += "\n"; } #endif }; // <<< int32_t main() { int n; cin >> n; double p,q; cin >> p >> q; if (p == 1) quit(1); Matrix A = { {q*q-p*p,p}, {-p,1} }; auto B = A.pow(n-1); dump(B); double x = B[0][0]*p + B[0][1]; double y = B[1][0]*p + B[1][1]; cout << x/y << endl; }