#pragma region Macros #pragma GCC optimize("O3") #include #define ll long long #define ld long double #define rep2(i,a,b) for(ll i=a;i<=b;++i) #define rep(i,n) for(ll i=0;i=b;--i) #define pii pair #define pll pair #define pb push_back #define eb emplace_back #define vi vector #define vec vector #define vll vector #define vpi vector #define vpll vector #define overload2(_1,_2,name,...) name #define vv(a,b) vector>(a,vector(b)) #define vv2(a,b,c) vector>(a,vector(b,c)) #define vvl(a,b) vector>(a,vector(b)) #define vvl2(a,b,c) vector>(a,vector(b,c)) #define vvv(a,b,c) vector(a) #define vvv2(a,b,c,d) vector(a) #define vvvl(a,b,c) vector(a) #define vvvl2(a,b,c,d) vector(a) #define fi first #define se second #define all(c) begin(c),end(c) #define ios ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0); #define lb(c,x) distance((c).begin(),lower_bound(all(c),(x))) #define ub(c,x) distance((c).begin(),upper_bound(all(c),(x))) using namespace std; template using pq = priority_queue; template using pqg = priority_queue,greater>; #define Size(c) (int)(c).size() #define INT(...) int __VA_ARGS__;IN(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;IN(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__;IN(__VA_ARGS__) #define STR(...) string __VA_ARGS__;IN(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;IN(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;IN(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;IN(__VA_ARGS__) #define VEC(type,name,size) vector name(size);IN(name) #define VV(type,name,h,w) vector>name(h,vector(w));IN(name) int scan(){ return getchar(); } void scan(int& a){ cin>>a; } void scan(long long& a){ cin>>a; } void scan(char &a){cin>>a;} void scan(double &a){ cin>>a; } void scan(long double& a){ cin>>a; } void scan(char a[]){ scanf("%s", a); } void scan(string& a){ cin >> a; } template void scan(vector&); template void scan(array&); template void scan(pair&); template void scan(T(&)[size]); template void scan(vector& a){ for(auto& i : a) scan(i); } template void scan(deque& a){ for(auto& i : a) scan(i); } template void scan(array& a){ for(auto& i : a) scan(i); } template void scan(pair& p){ scan(p.first); scan(p.second); } template void scan(T (&a)[size]){ for(auto& i : a) scan(i); } template void scan(T& a){ cin >> a; } void IN(){} template void IN(Head& head, Tail&... tail){ scan(head); IN(tail...); } string stin() {string s;cin>>s;return s;} template inline bool chmax(T& a,T b){if(a inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;} vi iota(int n){vi a(n);iota(all(a),0);return a;} template void UNIQUE(vector &x){sort(all(x));x.erase(unique(all(x)),x.end());} int in() {int x;cin>>x;return x;} ll lin() {unsigned long long x;cin>>x;return x;} void print(){putchar(' ');} void print(bool a){cout< void print(const vector&); template void print(const array&); template void print(const pair& p); template void print(const T (&)[size]); template void print(const vector& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout<<" "; print(*i); } cout< void print(const deque& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout<<" "; print(*i); } } template void print(const array& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout<<" "; print(*i); } } template void print(const pair& p){ cout<<'(';print(p.first); cout<<","; print(p.second);cout<<')'; } template void print(set &x){for(auto e:x)print(e),cout<<" ";cout< void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ cout<<" "; print(*i); } } template void print(const T& a){ cout << a; } int out(){ putchar('\n'); return 0; } template int out(const T& t){ print(t); putchar('\n'); return 0; } template int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; } ll gcd(ll a, ll b){ a = abs(a),b = abs(b);while(b){ ll c = b; b = a % b; a = c; } return a; } ll lcm(ll a, ll b){ if(!a || !b) return 0; return a * b / gcd(a, b); } vector factor(ll x){ vector ans; for(ll i = 2; i * i <= x; i++) if(x % i == 0){ ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; } vector divisor(int x){ vector ans; for(int i=1;i*i<=x;i++)if(x%i==0){ans.pb(i);if(i*i!=x)ans.pb(x/i);} return ans;} int popcount(ll x){return __builtin_popcountll(x);} mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); int rnd(int n){return uniform_int_distribution(0, n-1)(rng);} #define endl '\n' #ifdef _LOCAL #undef endl #define debug(x) cout<<#x<<": ";print(x);cout< void err(const T& t){ print(t); cout<<" ";} template void err(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); } #else #define debug(x) template void err(const T&...){} #endif struct Setup_io{ Setup_io(){ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0);cout< class modint { using u64 = ll; public: u64 a; constexpr modint(const u64 x = 0) noexcept : a(((x % Modulus) + Modulus)%Modulus) {} constexpr u64 &value() noexcept { return a; } constexpr const u64 &value() const noexcept { return a; } constexpr modint operator+(const modint rhs) const noexcept { return modint(*this) += rhs; } constexpr modint operator-(const modint rhs) const noexcept { return modint(*this) -= rhs; } constexpr modint operator*(const modint rhs) const noexcept { return modint(*this) *= rhs; } constexpr modint operator/(const modint rhs) const noexcept { return modint(*this) /= rhs; } constexpr modint &operator+=(const modint rhs) noexcept { a += rhs.a; if (a >= Modulus) { a -= Modulus; } return *this; } constexpr modint &operator-=(const modint rhs) noexcept { if (a < rhs.a) { a += Modulus; } a -= rhs.a; return *this; } constexpr modint &operator*=(const modint rhs) noexcept { a = a * rhs.a % Modulus; return *this; } constexpr modint &operator/=(modint rhs) noexcept { u64 exp = Modulus - 2; while (exp) { if (exp % 2) { *this *= rhs; } rhs *= rhs; exp /= 2; } return *this; } }; #define mint modint mint inv[N],comb[N],prd[N],invprd[N]; void calc_inv(){ inv[1]=1; rep2(i,2,N-1){ inv[i]=inv[MOD%i]*(-MOD/i); } return; } void calc_product(){ prd[0]=prd[1]=1; invprd[0]=invprd[1]=1; rep2(i,2,N-1){ prd[i]=prd[i-1]*i; invprd[i]=inv[i]*invprd[i-1]; } return ; } mint cmb(int a,int b){ if(a ; ostream& operator<<(ostream& os, mint a){ os << a.a ; return os; } template< class T > struct Matrix { vector< vector< T > > A; Matrix() {} Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {} Matrix(size_t n) : A(n, vector< T >(n, 0)) {}; size_t height() const { return (A.size()); } size_t width() const { return (A[0].size()); } inline const vector< T > &operator[](int k) const { return (A.at(k)); } inline vector< T > &operator[](int k) { return (A.at(k)); } static Matrix I(size_t n) { Matrix mat(n); for(int i = 0; i < n; i++) mat[i][i] = 1; return (mat); } Matrix &operator+=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); vector< vector< T > > C(n, vector< T >(m, 0)); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) for(int k = 0; k < p; k++) C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); A.swap(C); return (*this); } Matrix &operator^=(long long k) { Matrix B = Matrix::I(height()); while(k > 0) { if(k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return (*this); } Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); } friend ostream &operator<<(ostream &os, Matrix &p) { size_t n = p.height(), m = p.width(); for(int i = 0; i < n; i++) { os << "["; for(int j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "]\n" : ","); } } return (os); } T determinant() { Matrix B(*this); assert(width() == height()); T ret = 1; for(int i = 0; i < width(); i++) { int idx = -1; for(int j = i; j < width(); j++) { if(B[j][i] != 0) idx = j; } if(idx == -1) return (0); if(i != idx) { ret *= -1; swap(B[i], B[idx]); } ret *= B[i][i]; T vv = B[i][i]; for(int j = 0; j < width(); j++) { B[i][j] /= vv; } for(int j = i + 1; j < width(); j++) { T a = B[j][i]; for(int k = 0; k < width(); k++) { B[j][k] -= B[i][k] * a; } } } return (ret); } }; main(){ LL(n); Matrix mat(6,6); calc(); rep(i,6){ mat[i][0] = inv[6]; if(i!=5) mat[i][i+1] = 1; } mat^=n; cout << mat[0][0] << endl; }