#define _USE_MATH_DEFINES #include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; template using posteriority_queue = priority_queue, greater >; const int INF = 0x3f3f3f3f; const ll LINF = 0x3f3f3f3f3f3f3f3fLL; const double EPS = 1e-8; const int MOD = 1000000007; // const int MOD = 998244353; const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1}; const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; } template void unique(vector &a) { a.erase(unique(ALL(a)), a.end()); } struct IOSetup { IOSetup() { cin.tie(nullptr); ios_base::sync_with_stdio(false); cout << fixed << setprecision(20); } } iosetup; int mod = MOD; struct ModInt { unsigned val; ModInt(): val(0) {} ModInt(ll x) : val(x >= 0 ? x % mod : x % mod + mod) {} ModInt pow(ll exponent) { ModInt tmp = *this, res = 1; while (exponent > 0) { if (exponent & 1) res *= tmp; tmp *= tmp; exponent >>= 1; } return res; } ModInt &operator+=(const ModInt &x) { if((val += x.val) >= mod) val -= mod; return *this; } ModInt &operator-=(const ModInt &x) { if((val += mod - x.val) >= mod) val -= mod; return *this; } ModInt &operator*=(const ModInt &x) { val = static_cast(val) * x.val % mod; return *this; } ModInt &operator/=(const ModInt &x) { // assert(__gcd(static_cast(x.val), mod) == 1); unsigned a = x.val, b = mod; int u = 1, v = 0; while (b) { unsigned tmp = a / b; swap(a -= tmp * b, b); swap(u -= tmp * v, v); } return *this *= u; } bool operator==(const ModInt &x) const { return val == x.val; } bool operator!=(const ModInt &x) const { return val != x.val; } bool operator<(const ModInt &x) const { return val < x.val; } bool operator<=(const ModInt &x) const { return val <= x.val; } bool operator>(const ModInt &x) const { return val > x.val; } bool operator>=(const ModInt &x) const { return val >= x.val; } ModInt &operator++() { if (++val == mod) val = 0; return *this; } ModInt operator++(int) { ModInt res = *this; ++*this; return res; } ModInt &operator--() { val = (val == 0 ? mod : val) - 1; return *this; } ModInt operator--(int) { ModInt res = *this; --*this; return res; } ModInt operator+() const { return *this; } ModInt operator-() const { return ModInt(val ? mod - val : 0); } ModInt operator+(const ModInt &x) const { return ModInt(*this) += x; } ModInt operator-(const ModInt &x) const { return ModInt(*this) -= x; } ModInt operator*(const ModInt &x) const { return ModInt(*this) *= x; } ModInt operator/(const ModInt &x) const { return ModInt(*this) /= x; } friend ostream &operator<<(ostream &os, const ModInt &x) { return os << x.val; } friend istream &operator>>(istream &is, ModInt &x) { ll val; is >> val; x = ModInt(val); return is; } }; ModInt abs(const ModInt &x) { return x; } struct Combinatorics { int val; // "val!" and "mod" must be disjoint. vector fact, fact_inv, inv; Combinatorics(int val = 10000000) : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) { fact[0] = 1; FOR(i, 1, val + 1) fact[i] = fact[i - 1] * i; fact_inv[val] = ModInt(1) / fact[val]; for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i; FOR(i, 1, val + 1) inv[i] = fact[i - 1] * fact_inv[i]; } ModInt nCk(int n, int k) { if (n < 0 || n < k || k < 0) return ModInt(0); // assert(n <= val && k <= val); return fact[n] * fact_inv[k] * fact_inv[n - k]; } ModInt nPk(int n, int k) { if (n < 0 || n < k || k < 0) return ModInt(0); // assert(n <= val); return fact[n] * fact_inv[n - k]; } ModInt nHk(int n, int k) { if (n < 0 || k < 0) return ModInt(0); return (k == 0 ? ModInt(1) : nCk(n + k - 1, k)); } }; template struct Matrix { vector > dat; Matrix(int m, int n, T val = 0) : dat(m, vector(n, val)) {} int height() const { return dat.size(); } int width() const { return dat.front().size(); } Matrix pow(ll exponent) { int n = height(); Matrix tmp = *this, res(n, n, 0); REP(i, n) res[i][i] = 1; while (exponent > 0) { if (exponent & 1) res *= tmp; tmp *= tmp; exponent >>= 1; } return res; } inline const vector &operator[](const int idx) const { return dat[idx]; } inline vector &operator[](const int idx) { return dat[idx]; } Matrix &operator=(const Matrix &x) { int m = x.height(), n = x.width(); dat.resize(m, vector(n)); REP(i, m) REP(j, n) dat[i][j] = x[i][j]; return *this; } Matrix &operator+=(const Matrix &x) { int m = height(), n = width(); REP(i, m) REP(j, n) dat[i][j] += x[i][j]; return *this; } Matrix &operator-=(const Matrix &x) { int m = height(), n = width(); REP(i, m) REP(j, n) dat[i][j] -= x[i][j]; return *this; } Matrix &operator*=(const Matrix &x) { int m = height(), n = x.width(), l = width(); vector > res(m, vector(n, 0)); REP(i, m) REP(j, n) { REP(k, l) res[i][j] += dat[i][k] * x[k][j]; } swap(dat, res); return *this; } Matrix operator+(const Matrix &x) const { return Matrix(*this) += x; } Matrix operator-(const Matrix &x) const { return Matrix(*this) -= x; } Matrix operator*(const Matrix &x) const { return Matrix(*this) *= x; } }; int main() { // https://maspypy.com/%e5%a4%9a%e9%a0%85%e5%bc%8f%e3%83%bb%e5%bd%a2%e5%bc%8f%e7%9a%84%e3%81%b9%e3%81%8d%e7%b4%9a%e6%95%b0%ef%bc%88%ef%bc%93%ef%bc%89%e7%b7%9a%e5%bd%a2%e6%bc%b8%e5%8c%96%e5%bc%8f%e3%81%a8%e5%bd%a2%e5%bc%8f // 母関数 x/(1-x)(1+x)(1-3x+x^2) = x/(1-3x+3x^3-x^4) // b_n = 3b_{n-1} - 3b_{n-3} + b_{n-4} Matrix m(4, 4), f(4, 1); m.dat = { {3, 0, -3, 1}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0} }; f.dat = { {6}, {2}, {1}, {0} }; ll n; cin >> n; if (n <= 3) { cout << f[3 - n][0] << '\n'; } else { cout << (m.pow(n - 3) * f)[0][0] << '\n'; } return 0; }