#include using namespace std; typedef long long ll; class Rational { ll gcd_(ll num1, ll num2){ return num2 == 0 ? num1: gcd_(num2, num1 % num2); } void norm(){ ll gcd = gcd_(num, den); num /= gcd, den /= gcd; } public: ll num, den; Rational(ll n=0, ll d=1):num(n),den(d) { norm(); } const Rational operator+(const Rational &p)const{ Rational ret(num*p.den+p.num*den,den*p.den);ret.norm();return ret;} const Rational operator-(const Rational &p)const{ Rational ret(num*p.den-p.num*den,den*p.den);ret.norm();return ret;} const Rational operator-(void)const{ Rational ret(-num,den);ret.norm();return ret;} const Rational operator*(const Rational &p)const{ Rational ret(num*p.num, den*p.den);ret.norm();return ret;} const Rational operator/(const Rational &p)const{ Rational ret(num*p.den, den*p.num);ret.norm();return ret;} bool operator==(const Rational &p)const{return (num==p.num && den==p.den);} bool operator< (const Rational &p)const{return (num*p.den> N; Rational a[2]; a[0] = Rational(4); a[1] = Rational(3); if(N < 2){ printf("%.16Lf\n", (long double)a[N].num/a[N].den); return 0; } for(int i = 2; i <= N; i++){ Rational aa = a[1]*Rational(19,4) - a[0]*Rational(3); a[0] = a[1]; a[1] = aa; } printf("%.16Lf\n", (long double)a[1].num/a[1].den); }