#include #ifdef __LOCAL #define DBG(X) cout << #X << " = " << (X) << endl; #define SAY(X) cout << (X) << endl; #else #define DBG(X) #define SAY(X) #define NDEBUG #endif using namespace std; typedef int_fast32_t int32; typedef int_fast64_t int64; const int32 inf = 1e9+7; const int32 MOD = 1000000007; const int64 llinf = 1e18; #define YES(n) cout << ((n) ? "YES\n" : "NO\n" ) #define Yes(n) cout << ((n) ? "Yes\n" : "No\n" ) #define POSSIBLE(n) cout << ((n) ? "POSSIBLE\n" : "IMPOSSIBLE\n" ) #define ANS(n) cout << (n) << "\n" #define REP(i,n) for(int64 i=0;i<(n);++i) #define FOR(i,a,b) for(int64 i=(a);i<(b);i++) #define FORR(i,a,b) for(int64 i=(a);i>=(b);i--) #define all(obj) (obj).begin(),(obj).end() #define rall(obj) (obj).rbegin(),(obj).rend() #define fi first #define se second #define pb(a) push_back(a) typedef pair pii; typedef pair pll; template inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; } template struct ModInt{ int_fast64_t x; constexpr ModInt(int_fast64_t y = 0):x((y%mod+mod)%mod){} constexpr ModInt& operator+=(const ModInt& a){ if((x += a.x) >= mod) x -= mod; return *this; } constexpr ModInt& operator-=(const ModInt& a){ if((x -= a.x) < 0)x += mod; return *this; } constexpr ModInt& operator*=(const ModInt& a){ x = x * a.x % mod; return *this; } constexpr ModInt& operator/=(const ModInt& a){ *this *= a.inv(); return *this; } constexpr ModInt operator-() const { return ModInt(-x); } constexpr ModInt operator+(const ModInt& a) const { return ModInt(*this) += a; } constexpr ModInt operator-(const ModInt& a) const { return ModInt(*this) -= a; } constexpr ModInt operator*(const ModInt& a) const { return ModInt(*this) *= a; } constexpr ModInt operator/(const ModInt& a) const { return ModInt(*this) /= a; } constexpr ModInt operator++(){ *this += ModInt(1); return *this; } constexpr ModInt operator++(int){ ModInt old = *this; ++*this; return old; } constexpr ModInt operator--(){ *this -= ModInt(1); return *this; } constexpr ModInt operator--(int){ ModInt old = *this; --*this; return old; } constexpr bool operator==(const ModInt& a) const { return x == a.x; } constexpr bool operator!=(const ModInt& a) const { return x != a.x; } constexpr ModInt pow(int_fast64_t r) const { if(!r)return 1; ModInt res = pow(r>>1); res *= res; if(r & 1) res *= *this; return res; } constexpr ModInt inv() const { return pow(mod-2); } friend istream& operator>>(istream& is, ModInt& a){ int_fast64_t t; is >> t; a = ModInt(t); return is; } friend ostream& operator<<(ostream& os, const ModInt& a){ return os << a.x; } }; using mint = ModInt; 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 size() const { if(A.empty()) return 0; assert(A.size() == A[0].size()); return A.size(); } 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); } }; int main(){ cin.tie(0); ios::sync_with_stdio(false); int64 n; cin >> n; Matrix ft(4,1); ft[0][0] = 2; ft[1][0] = 3; ft[2][0] = 1; ft[3][0] = 1; Matrix E(4,4); E[0] = {0,1,0,1}; E[1] = {1,0,0,0}; E[2] = {0,1,0,0}; E[3] = {0,0,1,0}; Matrix O(4,4); O[0] = {1,1,1,1}; O[1] = {1,0,0,0}; O[2] = {0,1,0,0}; O[3] = {0,0,1,0}; if(n <= 4){ ANS(ft[4-n][0]); return 0; } auto EO = E * O; EO ^= (n-4)/2; if(n % 2)EO = O * EO; ANS((EO * ft)[0][0]); return 0; }