Submission #7423020

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Source Code Expand

#pragma GCC optimize("Ofast")
#include<bits/stdc++.h>
using namespace::std;
struct __INIT{__INIT(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}} __init;
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/numeric/interval.hpp>
#include <boost/numeric/interval/io.hpp>
// #include <boost/intrusive/rbtree.hpp>
// #include <boost/geometry.hpp>
// #include <boost/geometry/geometries/linestring.hpp>
// #include <boost/geometry/geometries/polygon.hpp>
// #include <boost/geometry/geometries/point_xy.hpp>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include<ext/pb_ds/tag_and_trait.hpp>
using namespace __gnu_pbds;
using namespace::std;
namespace mp = boost::multiprecision;
typedef mp::number<mp::cpp_dec_float<256,int64_t>> cdouble;
typedef mp::cpp_int cint;
typedef long long lint;
typedef long long ll;
typedef long double ldouble;
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<double> dvec;
typedef vector<vector<double>> dmat;
typedef vector<vector<vector<double>>> dmat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
typedef vector<vector<vector<string>>> smat3;
typedef vector<pair<lint,lint>> pvec;
typedef vector<vector<pair<lint,lint>>> pmat;
typedef vector<vector<vector<pair<lint,lint>>>> pmat3;
#define rep(i, n) for(lint i = 0; i < (lint)(n); i++)
#define irep(i) for(lint i = 0;; i++)
#define irep1(i) for(lint i = 1;; i++)
#define irep2(i) for(lint i = 2;; i++)
#define rrep(i, n) for(lint i = (lint)(n-1); i >-1; i--)
#define rrepi(i,a,b) for(lint i = (lint)(b-1); i >a-1; i--)
#define repi(i,a,b) for(lint i=lint(a);i<lint(b);i++)
#define rep2(i,a,b,c) for(lint i=lint(a);i>lint(b);i+=c)
#define all(x) (x).begin(),(x).end()
#define PI 3.141592653589793
#define dist(x1,y1,x2,y2) (pow(pow(x2-x1,2)+pow(y2-y1,2),0.5))
#define output(v) do{bool f=0;for(auto i:v){cout<<(f?" ":"");if(i>INF/2)cout<<"INF";else cout<<i;f=1;}cout<<"\n";}while(0)
#define output2(v) for(auto j:v)output(j);
#define input(a,n) lint n;cin>>n;vector<lint>a(n);rep(i,n)cin>>a[i];
#define SUM(v) accumulate(all(v),0LL)
#define INF (1LL<<60)
#define IINF (1<<30)
#define EPS (1e-10)
#define LINF 9223372036854775807
#define MOD 1000000007
#define endl "\n"
struct any{
    string s;
    any(string s):s(s){}
    operator lint()const{return stoll(s);}
    operator double()const{return stod(s);}
    operator string()const{return s;}
};
any in(void){
    return any(*istream_iterator<string>(cin));
}
inline lint gcd(lint a,lint b){return b?gcd(b,a%b):a;}
inline lint lcm(lint a,lint b){return a*b/gcd(a,b);}
inline bool chmin(auto& s,const auto& t){bool res=s>t;s=min(s,t);return res;}
inline bool chmax(auto& s,const auto& t){bool res=s<t;s=max(s,t);return res;}
inline lint mex(vector<lint> s){
    lint res=0;
    sort(all(s));
    while(binary_search(all(s),res))res++;
    return res;
}
vector<lint> dx={-1,1,0,0,1,1,-1,-1};
vector<lint> dy={0,0,-1,1,1,-1,1,-1};

struct BIT{
    private:
    vector<lint> bit,bit2;
    lint n;
    public:
    BIT(lint n):n(n){
        bit.resize(n+1,0);
        bit2.resize(n+1,0);
    }
    //0-indexed [0,x)-sum
    lint sum(lint x){
        lint res=0;
        for(lint i=x;i>0;i-=i&-i)res+=bit[i];
        for(lint i=x;i>0;i-=i&-i)res+=x*bit2[i];
        return res;
    }
    //0-indexed [x,y)-sum
    lint sum(lint x,lint y){
        return sum(y)-sum(x);
    }
    //0-indexed [l,r)add
    void add(lint l,lint r,lint x){
        l++;r++;
        if(0>r||l>n)return;
        for(lint i=l;i<=n;i+=i&-i)bit[i]+=-x*(l-1);
        for(lint i=r;i<=n;i+=i&-i)bit[i]+=x*r;
        for(lint i=l;i<=n;i+=i&-i)bit2[i]+=x;
        for(lint i=r;i<=n;i+=i&-i)bit2[i]+=-x;
    }
};
// struct tree{
//     private:
//     lint n;
//     vector<>
//     public:
//     tree(lint n):n(n){}
//     tree addEdge(lint from,lint to,lint cost=1){
        
//     }
// }
lint comb(lint a,lint b){
    cint ans=1;
    repi(i,a-b+1,a+1){
        ans*=i;
    }
    repi(i,1,b+1){
        ans/=i;
    }
    return (lint)ans;
}
int main(){
    lint n;
    cin>>n;
    vector<cdouble> dp(n+1,0);
    repi(i,2,n+1){
        //j:グー,k:チョキ,l:パー
        cdouble aiko=0;
        cdouble kitai=0;
        cdouble waight=1;
        rep(j,i+1){
            waight=comb(i,j);
            rep(k,i-j+1){
                if(k!=0){
                    waight*=i-j-k+1;
                    waight/=k;
                }
                lint l=i-j-k;
                vec v={j,k,l};
                set<lint> s{j,k,l};
                s.erase(0);
                sort(all(v));
                if((v[0]==0&&v[1]==0)||(v[0]==v[1]&&v[1]==v[2])){
                    aiko+=waight;
                }else{
                    kitai+=(dp[*min_element(all(s))]+1)*waight;
                }
            }
        }
        dp[i]=(aiko+kitai)/(pow(cdouble(3),cdouble(i))-aiko);
    }
    cout<<dp[n];
}

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