#pragma GCC optimize ("O3") #include "bits/stdc++.h" using namespace std; using ll = long long int; #define debugos cout #define debug(v) {printf("L%d %s > ",__LINE__,#v);debugos<<(v)< ",__LINE__,#v);for(auto e:(v)){debugos< ",__LINE__,#m);for(int x=0;x<(w);x++){debugos<<(m)[x]<<" ";}debugos<\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){debugos<<(m)[y][x]<<" ";}debugos<::type>::type cnt=0;(cnt)<(l);++(cnt)) #define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt)) #define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt)) #define diterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);--(cnt)) const ll MD = 1000000007ll; const long double PI = 3.1415926535897932384626433832795L; inline void assert_call(bool assertion, function f) { if (!assertion) { cerr << "assertion fault:" << endl; f(); abort(); } } template inline ostream& operator <<(ostream &o, const pair p) { o << '(' << p.first << ':' << p.second << ')'; return o; } template inline ostream& _ostream_vecprint(ostream& os, const Vec& a) { os << '['; for (const auto& e : a) os << ' ' << e << ' '; os << ']'; return os; } template inline ostream& operator<<(ostream& o, const vector& v) { return _ostream_vecprint(o, v); } template inline ostream& operator<<(ostream& o, const array& v) { return _ostream_vecprint(o, v); } template inline T& maxset(T& to, const T& val) { return to = max(to, val); } template inline T& minset(T& to, const T& val) { return to = min(to, val); } void bye(string s, int code = 0) { cout << s << endl; exit(code); } mt19937_64 randdev(8901016); template inline T rand(T l, T h) { return uniform_int_distribution(l, h)(randdev); } template<> inline double rand(double l, double h) { return uniform_real_distribution(l, h)(randdev); } template<> inline float rand(float l, float h) { return uniform_real_distribution(l, h)(randdev); } #if defined(_WIN32) || defined(_WIN64) #define getchar_unlocked _getchar_nolock #define putchar_unlocked _putchar_nolock #elif defined(__GNUC__) #else #define getchar_unlocked getchar #define putchar_unlocked putchar #endif namespace { #define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E) class MaiScanner { public: template void input_integer(T& var) { var = 0; T sign = 1; int cc = getchar_unlocked(); for (; cc<'0' || '9'>(int& var) { input_integer(var); return *this; } inline MaiScanner& operator>>(long long& var) { input_integer(var); return *this; } inline MaiScanner& operator>>(string& var) { int cc = getchar_unlocked(); for (; !isvisiblechar(cc); cc = getchar_unlocked()); for (; isvisiblechar(cc); cc = getchar_unlocked()) var.push_back(cc); return *this; } template void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; } }; class MaiPrinter { public: template void output_integer(T var) { if (var == 0) { putchar_unlocked('0'); return; } if (var < 0) putchar_unlocked('-'), var = -var; char stack[32]; int stack_p = 0; while (var) stack[stack_p++] = '0' + (var % 10), var /= 10; while (stack_p) putchar_unlocked(stack[--stack_p]); } inline MaiPrinter& operator<<(char c) { putchar_unlocked(c); return *this; } inline MaiPrinter& operator<<(int var) { output_integer(var); return *this; } inline MaiPrinter& operator<<(long long var) { output_integer(var); return *this; } inline MaiPrinter& operator<<(char* str_p) { while (*str_p) putchar_unlocked(*(str_p++)); return *this; } inline MaiPrinter& operator<<(const string& str) { const char* p = str.c_str(); const char* l = p + str.size(); while (p < l) putchar_unlocked(*p++); return *this; } template void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin : *this << *begin; } }; } MaiScanner scanner; MaiPrinter printer; template // typedef double T; class Matrix { public: size_t height_, width_; valarray data_; Matrix(size_t height, size_t width) :height_(height), width_(width), data_(height*width) {} Matrix(size_t height, size_t width, const valarray& data) :height_(height), width_(width), data_(data) {} inline T& operator()(size_t y, size_t x) { return data_[y*width_ + x]; } inline T operator() (size_t y, size_t x) const { return data_[y*width_ + x]; } inline T& at(size_t y, size_t x) { return data_[y*width_ + x]; } inline T at(size_t y, size_t x) const { return data_[y*width_ + x]; } inline void resize(size_t h, size_t w) { height_ = h; width_ = w; data_.resize(h*w); } inline void resize(size_t h, size_t w, T val) { height_ = h; width_ = w; data_.resize(h*w, val); } inline void fill(T val) { data_ = val; } Matrix& setDiag(T val) { for (size_t i = 0, en = min(width_, height_); i < en; ++i)at(i, i) = val; return *this; } void print(ostream& os) { os << "- - -" << endl; // << setprecision(3) for (size_t y = 0; y < height_; ++y) { for (size_t x = 0; x < width_; ++x) { os << setw(7) << at(y, x) << ' '; }os << endl; } } valarray> to_valarray() const { valarray> work(height_); for (size_t i = 0; i < height_; ++i) { auto &v = work[i]; v.resize(height_); for (size_t j = 0; j < width_; ++j) v[j] = at(i, j); } return work; } // mathematics Matrix pow(long long); double det() const; T tr(); Matrix& transpose_self(); Matrix transpose() const; struct LU { size_t size; vector pivot; vector elem; }; }; // IO template inline ostream& operator << (ostream& os, Matrix mat) { mat.print(os); return os; } // 掛け算 template Matrix multiply(const Matrix& mat1, const Matrix& mat2) { assert(mat1.width_ == mat2.height_); Matrix result(mat1.height_, mat2.width_); for (size_t i = 0; i < mat1.height_; i++) { for (size_t j = 0; j < mat2.width_; j++) { for (size_t k = 0; k < mat1.width_; k++) { result(i, j) += mat1(i, k) * mat2(k, j); } } } return result; } template valarray multiply(const Matrix& mat1, const valarray& vec2) { assert(mat1.width_ == vec2.size()); valarray result(mat1.height_); for (size_t i = 0, j; i < mat1.height_; i++) { for (j = 0; j < mat1.width_; j++) { result[i] += mat1(i, j) * vec2[j]; } } return result; } template inline Matrix& operator*=(Matrix& mat1, Matrix& mat2) { mat1 = multiply(mat1, mat2); return mat1; } template inline Matrix operator*(Matrix& mat1, Matrix& mat2) { return multiply(mat1, mat2); } // スカラー template inline Matrix& operator+=(Matrix& mat, T val) { mat.data_ += val; return mat; } template inline Matrix& operator*=(Matrix& mat, T val) { mat.data_ *= val; return mat; } template inline Matrix& operator/=(Matrix& mat, T val) { mat.data_ /= val; return mat; } template inline Matrix& operator^=(Matrix& mat, T val) { mat.data_ ^= val; return mat; } // 行列 template inline Matrix& operator+=(Matrix& mat1, Matrix& mat2) { mat1.data_ += mat2.data_; return mat1; } template inline Matrix operator+(Matrix& mat1, Matrix& mat2) { return Matrix(mat1.height_, mat1.width_, mat1.data_ + mat2.data_); } template Matrix Matrix::pow(long long p) { assert(height_ == width_); Matrix a = *this; Matrix b(height_, height_); b.setDiag(1); while (0 < p) { if (p % 2) { b *= a; } a *= a; p /= 2; } return b; } class llmod { private: ll val_; inline ll cut(ll v) const { return ((v%MOD) + MOD) % MOD; } public: static const ll MOD = MD; // <= llmod() : val_(0) {} llmod(ll num) :val_(cut(num)) {} llmod(const llmod& lm) : val_(lm.val_) {} inline operator ll() const { return val_; } inline ll operator *() const { return val_; } inline llmod& operator=(const llmod& lm) { val_ = lm.val_; return *this; } inline llmod& operator=(ll v) { val_ = cut(v); return *this; } inline llmod& operator+=(ll v) { val_ = cut(val_ + v); return *this; } inline llmod& operator+=(const llmod& l) { val_ = cut(val_ + l.val_); return *this; } inline llmod& operator-=(ll v) { val_ = cut(val_ - v); return *this; } inline llmod& operator-=(const llmod& l) { val_ = cut(val_ - l.val_); return *this; } inline llmod& operator*=(ll v) { val_ = cut(val_ * v); return *this; } inline llmod& operator*=(const llmod& l) { val_ = cut(val_ * l.val_); return *this; } inline llmod& operator++() { val_ = (val_ + 1) % MOD; return *this; } inline llmod operator++(int) { llmod t = *this; val_ = (val_ + 1) % MOD; return t; } }; inline ostream& operator<<(ostream& os, const llmod& l) { os << *l; return os; } inline llmod operator+(llmod t, const llmod& r) { return t += r; } inline llmod operator-(llmod t, const llmod& r) { return t -= r; } inline llmod operator*(llmod t, const llmod& r) { return t *= r; } // MEMO : 逆元...powm(n,MD-2) llmod pow(llmod x, ll p) { llmod y = 1; while (0 < p) { if (p % 2) y *= x; x *= x; p /= 2; } return y; } inline llmod& operator/=(llmod& l, const llmod& r) { return l *= pow(r, llmod::MOD - 2); } int main() { ll N; cin >> N; if (N < 3) { vector hoge = {0,1,2}; cout << hoge[N] << endl; return 0; } Matrix mat(4, 4, { 1,1,2,0, 1,0,0,0, 1,0,1,0, 1,1,2,1}); auto mp = mat.pow(N-2); valarray v = {1,1,1,2}; auto w = multiply(mp, v); cout << *w[3] << endl; return 0; }