#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using pii = pair; using ll=long long; using ld=long double; #define pb push_back #define mp make_pair #define sc second #define fr first #define stpr setprecision #define cYES cout<<"YES"<=0;i--) #define rRep(i,a,b) for(ll i=a;i>=b;i--) #define crep(i) for(char i='a';i<='z';++i) #define psortsecond(A,N) sort(A,A+N,[](const pii &a, const pii &b){return a.second inline bool chmax(T& lhs, const U& rhs) { if (lhs < rhs) { lhs = rhs; return 1; } return 0; } template inline bool chmin(T& lhs, const U& rhs) { if (lhs > rhs) { lhs = rhs; return 1; } return 0; } template istream& operator>>(istream& is,vector& v){for(auto&& x:v)is >> x;return is;} template istream& operator>>(istream& is, pair& p){ is >> p.first; is >> p.second; return is;} template ostream& operator>>(ostream& os, const pair& p){ os << p.first << ' ' << p.second; return os;} template ostream& operator<<(ostream& os, vector& v){ for(auto i=begin(v); i != end(v); ++i){ if(i !=begin(v)) os << ' '; os << *i; } return os; } // modint template class modint { using u64 = std::uint_fast64_t; public: u64 a; constexpr modint(const u64 x = 0) noexcept : a(x % 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; } }; void printVector(vector a, int x){//ベクトル出力 有効数字x桁 rep(i,a.size()){ cout << stpr(x) << a[i] << endl; } } void printMatrix(vector> a,int x){//行列出力 有効数字x桁 rep(i,a.size()){ rep(j,a[i].size()){ cout << stpr(x) << a[i][j] << " "; } cout << endl; } } vector VectorAdd(vector a,vector b){ vector c(a.size()); rep(i,a.size()){ c[i]=a[i]+b[i]; } return c; } vector VectorSubtract(vector a,vector b){ vector c(a.size()); rep(i,a.size()){ c[i]=a[i]-b[i]; } return c; } vector VectorMultiply(vector a,int b){ vector c(a.size()); rep(i,a.size()){ c[i]=a[i]*b; } return c; } vector> MatrixSubtract(vector> a,vector> b){ vector> c(a.size(),vector(a[0].size())); rep(i,a.size()){ rep(j,a[i].size()){ c[i][j]=a[i][j]-b[i][j]; } } return c; } vector> MatrixAdd(vector> a,vector> b){ // 行列と行列の和 // a.size() = aの行数  // a[0].size() = aの列数  vector> c(a.size(),vector(a[0].size())); // 行数がa.size()、列数がa[0].size()の配列の配列を確保する rep(i,a.size()){ rep(j,a[i].size()){ c[i][j]=a[i][j]+b[i][j]; } } return c; // 行列を返す } vector> IntMatrixMultiply(vector> a,int b){ vector> c(a.size(),vector(a[0].size())); rep(i,a.size()){ rep(j,a[i].size()){ c[i][j]=a[i][j]*b; } } return c; } vector MatrixVectorMultiply(vector> a,vector b){ vector c(a.size()); rep(i,a.size()){ double sum=0; rep(j,a[i].size()){ sum+=a[i][j]*b[j]; } c[i]=sum; } return c; } vector VectorMatrixMultiply(vector a,vector> b){ vector c(b[0].size()); rep(i,b[0].size()){ double sum=0; rep(j,a.size()){ sum+=a[j]*b[j][i]; } c[i]=sum; } return c; } vector> MatrixMatrixMultiply(vector> a,vector> b){ vector> c(a.size(),vector(b[0].size(),0.0)); rep(i,a.size()){ rep(j,b[0].size()){ rep(k,a[0].size()){ c[i][j]+=a[i][k]*b[k][j]; } } } return c; } double VectorNorm1(vector a){ double norm = 0; rep(i,a.size()){ norm+=fabs(a[i]); } return norm; } double VectorNorm2(vector a){ double norm = 0; rep(i,a.size()){ norm+=a[i]*a[i]; } return sqrt(norm); } double VectorNormInfinity(vector a){ double norm = 0; rep(i,a.size()){ norm=max(norm,a[i]); } return norm; } double MatrixNorm1(vector> a){ double norm = 0; rep(i,a[0].size()){ double sum=0; rep(j,a.size()){ sum+=fabs(a[j][i]); } norm=max(norm,sum); } return norm; } double MatrixNormInfinity(vector> a){ double norm = 0; rep(i,a.size()){ double sum=0; rep(j,a[i].size()){ sum+=fabs(a[i][j]); } norm=max(norm,sum); } return norm; } void PreDelete(vector> &a,vector &b){ //前進消去過程 rep(i,a.size()-1){ Rep(j,i+1,a.size()){ double X=a[j][i]/a[i][i]; rep(k,a.size()+1){ a[j][k]-=a[i][k]*X; } b[j]-=b[i]*X; } } } void BackReplace(vector> &a,vector &b){ //後退代入過程 rrep(i,a.size()){ double key=b[i]; if(i==a.size()-1){ b[i]=b[i]/a[i][i]; } else{ Rep(j,i+1,a.size()){ key-=a[i][j]*b[j]; } b[i]=key/a[i][i]; } } } vector> LUdecompfirst(vector> a){ // LU分解の行列を作るまで vector> C(a.size(),vector(a.size(),0)),LU(a.size()); rep(key,a.size()-1){ rep(i,a.size()){ rep(j,a.size()){ if(j>i) C[i][j]=0; else if(j==i) C[i][j]=1; else if(key==j) C[i][j]=-a[i][j]/a[j][j]; else C[i][j]=0; } } a = MatrixMatrixMultiply(C,a); Rep(i,key,a.size()) LU[key].pb(a[key][i]); Rep(i,key+1,a.size()) LU[i].pb(-C[i][key]); } LU[a.size()-1].pb(a[a.size()-1][a.size()-1]); return LU; } vector LUdecompsecond(vector> LU,vector B){ // LU分解の行列を使って解を求める vector x(LU.size(),0); vector y; rep(i,LU.size()){ double SUM=B[i]; rep(j,i) SUM-=LU[i][j]*y[j]; y.pb(SUM); } rrep(i,LU.size()){ double SUM=y[i]; Rep(j,i,LU.size()) SUM-=LU[i][j]*x[j]; SUM/=LU[i][i]; x[i]=SUM; } return x; } vector> Multiply_Matrix(ll lx,ll ly,ll ry,vector> A_,vector> B_,ll m){ //(左の行数、左の列数、右の列数、A、B、法とするmod(modを取らないときは-1) vector> V_ (lx,vector (ry,0)); rep(i,lx){ rep(j,ry){ rep(k,ly){ V_[i][j]+=A_[i][k]*B_[k][j]; if(m!=-1){ V_[i][j]%=m; } } } } return V_; } // 行列累乗(上とセットで使う) vector> Matrix_Modpow(ll ms,vector> A,ll e,ll m){ // サイズmsの正方行列Aのe乗をmod mで求める(modを取らないときはm=-1) if(e==1){ return A; } vector> cme = Matrix_Modpow(ms,A,e/2,m); cme = Multiply_Matrix(ms,ms,ms,cme,cme,m); if(e%2==1) cme = Multiply_Matrix(ms,ms,ms,cme,A,m); return cme; } int main(){ ll N;cin>>N; vector> V(4,vector(4,1)); V[0][0]=0;V[1][1]=0;V[2][2]=0;V[3][3]=0; auto Y=Matrix_Modpow(4,V,N,MOD); cout<