#include using namespace std; typedef long long ll; typedef long double ld; #define inf 1000000007 #define MP make_pair #define MT make_tuple #define PB push_back #define fi first #define se second #define rep(i,n) for(int i = 0; i < (int)(n); ++i) #define rrep(i,n) for(int i = (int)n-1; i >= 0; --i) #define srep(i,a,b) for(int i = (int)a; i < (int)(b); ++i) #define all(x) (x).begin(),(x).end() #define SUM(v) accumulate(all(v), 0LL) #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define lb(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define ub(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()) #define SZ(c) (int)(c).size() template ostream& operator << (ostream& os, vector& vec) { os << "{"; for (int i = 0; i<(int)vec.size(); i++) { os << vec[i] << (i + 1 == (int)vec.size() ? "" : ", "); } os << "}"; return os; } // pair出力 template ostream& operator << (ostream& os, pair pair_var) { os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map出力 template ostream& operator << (ostream& os, map& map_var) { os << "{"; for(auto itr = map_var.begin(); itr != map_var.end(); itr++){ os << "(" << itr->first << ", " << itr->second << ")"; itr++; if(itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } // set 出力 template ostream& operator << (ostream& os, set& set_var) { os << "{"; for(auto itr = set_var.begin(); itr != set_var.end(); itr++){ os << (*itr); ++itr; if(itr != set_var.end()) os << ", "; itr--; } os << "}"; return os; } // tuple 出力 template void out(ostream &os,const Tuple &t){} template void out(ostream &os,const Tuple &t){ if(N)os<<", "; os<(t); out(os,t); } template ostream& operator<<(ostream &os, const tuple &t){ os<<"("; out<0,tuple,Ts...>(os,t); os<<")"; return os; } #define overload2(_1, _2, name, ...) 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(string &a) { cin >> a; } template void scan(pair &p) { scan(p.first), scan(p.second); } template void scan(vector &); template void scan(vector &a) { 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...); } const string YESNO[2] = {"NO", "YES"}; const string YesNo[2] = {"No", "Yes"}; const string yesno[2] = {"no", "yes"}; void YES(bool t = 1) { cout << YESNO[t] << endl; } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { cout << YesNo[t] << endl; } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { cout << yesno[t] << endl; } void no(bool t = 1) { yes(!t); } #ifdef LOCAL void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << " " << H; debug_out(T...); } #define dbg(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define dbg(...) (void(0)) #define dump(x) (void(0)) #endif template std::enable_if_t::value> fill(A& array, const T& val) { array = val; } template std::enable_if_t::value> fill(A& array, const T& val) { for (auto& a : array) { fill(a, val); } } template T ceil(T x, S y) { assert(y); return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y)); } template T floor(T x, S y) { assert(y); return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1))); } vector iota(int n) {vector a(n);iota(all(a), 0);return a;} template T POW(T x, int n) {T res = 1;for(; n; n >>= 1, x *= x){if(n & 1) res *= x;}return res;} ll pow2(int i) { return 1LL << i; } int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); } int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); } int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); } int lowbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); } // int allbit(int n) { return (1 << n) - 1; } ll allbit(ll n) { return (1LL << n) - 1; } int popcount(signed t) { return __builtin_popcount(t); } int popcount(ll t) { return __builtin_popcountll(t); } bool ispow2(int i) { return i && (i & -i) == i; } template void fold_in(vector &v) {} template void fold_in(vector &v, Head &&a, Tail &&...tail) { for(auto e : a) v.emplace_back(e); fold_in(v, tail...); } template void renumber(vector &v) {} template void renumber(vector &v, Head &&a, Tail &&...tail) { for(auto &&e : a) e = lb(v, e); renumber(v, tail...); } template void zip(vector &head, Args &&...args) { vector v; fold_in(v, head, args...); sort(all(v)), v.erase(unique(all(v)), v.end()); renumber(v, head, args...); } template inline bool chmax(T &a, T b){ if(a inline bool chmin(T &a, T b){ if(a>b){ a = b; return true; } return false; } #define MOD 1000000007 template class ModInt { private: unsigned int v; static unsigned int norm(const unsigned int& x){ return x < mod ? x : x - mod; } static ModInt make(const unsigned int& x){ ModInt m; return m.v = x, m; } static ModInt inv(const ModInt& x){ return make(inverse(x.v, mod)); } static unsigned int inverse(int a, int m){ int u[] = {a, 1, 0}, v[] = {m, 0, 1}, t; while(*v){ t = *u / *v; swap(u[0] -= t * v[0], v[0]), swap(u[1] -= t * v[1], v[1]), swap(u[2] -= t * v[2], v[2]); } return (u[1] % m + m) % m; } public: ModInt() : v{0}{} ModInt(const long long val) : v{norm(val % mod + mod)} {} ModInt(const ModInt& n) : v{n()} {} explicit operator bool() const noexcept { return v != 0; } bool operator!() const noexcept { return !static_cast(*this); } ModInt& operator=(const ModInt& n){ return v = n(), (*this); } ModInt& operator=(const long long val){ return v = norm(val % mod + mod), (*this); } ModInt operator+() const { return *this; } ModInt operator-() const { return v == 0 ? make(0) : make(mod - v); } ModInt operator+(const ModInt& val) const { return make(norm(v + val())); } ModInt operator-(const ModInt& val) const { return make(norm(v + mod - val())); } ModInt operator*(const ModInt& val) const { return make((long long)v * val() % mod); } ModInt operator/(const ModInt& val) const { return *this * inv(val); } ModInt& operator+=(const ModInt& val){ return *this = *this + val; } ModInt& operator-=(const ModInt& val){ return *this = *this - val; } ModInt& operator*=(const ModInt& val){ return *this = *this * val; } ModInt& operator/=(const ModInt& val){ return *this = *this / val; } ModInt operator+(const long long val) const { return ModInt{v + val}; } ModInt operator-(const long long val) const { return ModInt{v - val}; } ModInt operator*(const long long val) const { return ModInt{(long long)(v * (val % mod))}; } ModInt operator/(const long long val) const { return ModInt{(long long)v * inv(val)}; } ModInt& operator+=(const long long val){ return *this = *this + val; } ModInt& operator-=(const long long val){ return *this = *this - val; } ModInt& operator*=(const long long val){ return *this = *this * val; } ModInt& operator/=(const long long val){ return *this = *this / val; } bool operator==(const ModInt& val) const { return v == val.v; } bool operator!=(const ModInt& val) const { return !(*this == val); } bool operator==(const long long val) const { return v == norm(val % mod + mod); } bool operator!=(const long long val) const { return !(*this == val); } unsigned int operator()() const { return v; } friend ModInt operator+(const long long val, const ModInt& n) { return n + val; } friend ModInt operator-(const long long val, const ModInt& n) { return ModInt{val - n()}; } friend ModInt operator*(const long long val, const ModInt& n) { return n * val; } friend ModInt operator/(const long long val, const ModInt& n) { return ModInt{val} / n; } friend bool operator==(const long long val, const ModInt& n) { return n == val; } friend bool operator!=(const long long val, const ModInt& n) { return !(val == n); } friend istream& operator>>(istream& is, ModInt& n){ unsigned int v; return is >> v, n = v, is; } friend ostream& operator<<(ostream& os, const ModInt& n){ return (os << n()); } friend ModInt mod_pow(ModInt x, long long n){ ModInt ans = ((mod == 1) ? 0 : 1); while(n){ if(n & 1) ans *= x; x *= x, n >>= 1; } return ans; } }; template class mat : public vector > { private: int r, c; //行,列 public: inline int row() const { return r; } inline int column() const { return c; } mat(int n, int m, T val = 0){ r = n, c = m; for(int i = 0; i < n; i++){ this->push_back(vector(m, val)); } } mat operator+(const mat& another) const { if(r != another.r && c != another.c){ cout << "足し算失敗(サイズ不一致)" << endl; exit(1); } mat X(r, c); for(int i = 0; i < r; i++){ for(int j = 0; j < c; j++){ X[i][j] = (*this)[i][j] + another[i][j]; } } return X; } mat operator+(const T val) const { mat X(r, c); for(int i = 0; i < r; i++){ for(int j = 0; j < c; j++){ X[i][j] = (*this)[i][j] + val; } } return X; } mat operator-(const mat& another) const { if(r != another.r && c != another.c){ cout << "引き算失敗(サイズ不一致)" << endl; exit(1); } mat X(r, c); for(int i = 0; i < r; i++){ for(int j = 0; j < c; j++){ X[i][j] = (*this)[i][j] - another[i][j]; } } return X; } mat operator-(const T val) const { mat X(r, c); for(int i = 0; i < r; i++){ for(int j = 0; j < c; j++){ X[i][j] = (*this)[i][j] - val; } } return X; } vector operator*(const vector& another) const { if(c != (int)another.size()){ cout << "掛け算失敗(サイズ不一致)" << endl; exit(1); } vector vec(r,0); for(int i = 0; i < r; i++){ for(int j = 0; j < c; j++){ vec[i] += (*this)[i][j] * another[j]; } } return vec; } mat operator*(const mat& another) const { if(c != another.r){ cout << "掛け算失敗(サイズ不一致)" << endl; exit(1); } mat X(r, another.c); for(int i = 0; i < r; i++){ for(int k = 0; k < c; k++){ for(int j = 0; j < (another.c); j++){ X[i][j] += (*this)[i][k] * another[k][j]; } } } return X; } mat operator-() const { mat X(r, c); for(int i = 0; i < r; i++){ for(int j = 0; j < c; j++){ X[i][j] = -(*this)[i][j]; } } return X; } int rank() const { int res = 0; mat B(r, c); for(int i = 0; i < r; i++){ for(int j = 0; j < c; j++){ B[i][j] = (*this)[i][j]; } } for(int i = 0; i < c; i++){ if(res == r) return res; int pivot = res; for(int j = res; j < r; j++){ if(B[j][i]){ pivot = j; break; } } if(!B[pivot][i]) continue; swap(B[pivot], B[res]); const T d = (T)1 / B[res][i]; for(int j = i + 1; j < c; j++){ B[res][j] *= d; } for(int j = res + 1; j < r; j++){ if(!B[j][i]) continue; for(int k = i + 1; k < c; k++){ B[j][k] -= B[res][k] * B[j][i]; } } ++res; } return res; } T det() const { if(r != c){ cout << "正方行列でない(行列式定義不可)" << endl; exit(1); } T ans = 1; mat B(r, r); for(int i = 0; i < r; i++){ for(int j = 0; j < c; j++){ B[i][j] = (*this)[i][j]; } } for(int i = 0; i < c; i++){ int pivot = i; for(int j = i; j < r; j++){ if(B[j][i]){ pivot = j; break; } } if(!B[pivot][i]) return (T)0; if(pivot != i) swap(B[i], B[pivot]), ans = -ans; ans *= B[i][i]; const T d = (T)1 / B[i][i]; for(int j = i + 1; j < c; j++){ B[i][j] *= d; } for(int j = i + 1; j < r; j++){ if(!B[j][i]) continue; for(int k = i + 1; k < c; k++){ B[j][k] -= B[i][k] * B[j][i]; } } } return ans; } mat inverse() const { if(r != c){ cout << "正方行列でない(逆行列定義不可)" << endl; exit(1); } mat B(r, 2*r); for(int i = 0; i < r; i++){ for(int j = 0; j < r; j++){ B[i][j] = (*this)[i][j]; } } for(int i = 0; i < r; i++){ B[i][r+i] = 1; } for(int i = 0; i < r; i++){ int pivot = i; for(int j = i; j < r; j++){ if(B[j][i]){ pivot = j; break; } } if(!B[pivot][i]){ cout << "正則でない" << endl; exit(1); } swap(B[i], B[pivot]); const T d = (T)1 / B[i][i]; for(int j = i + 1; j < 2*r; j++){ B[i][j] *= d; } for(int j = 0; j < r; j++){ if(j == i || !B[j][i]) continue; for(int k = i + 1; k < 2*r; k++){ B[j][k] -= B[i][k] * B[j][i]; } } } mat res(r, r); for(int i = 0; i < r; i++){ for(int j = 0; j < r; j++){ res[i][j] = B[i][r+j]; } } return res; } inline void print() const { for(int i = 0; i < r; i++){ for(int j = 0; j < (c-1); j++){ cout << (*this)[i][j] << ","; } cout << (*this)[i][c-1] << endl; } } }; template vector eq_solve(const mat& A, const vector& b){ if(A.row() != A.column()){ cout << "正方行列でない(解なしor不定)" << endl; exit(1); } int n = A.row(); mat B(n, n+1); for(int i = 0; i < n; i++){ for(int j = 0; j < n; j++){ B[i][j] = A[i][j]; } } for(int i = 0; i < n; i++){ B[i][n] = b[i]; } for(int i = 0; i < n; i++){ int pivot = i; for(int j = i; j < n; j++){ if(B[j][i]){ pivot = j; break; } } if(!B[pivot][i]){ cout << "解なしor不定" << endl; exit(1); } swap(B[i], B[pivot]); const T d = (T)1 / B[i][i]; for(int j = i + 1; j <= n; j++){ B[i][j] *= d; } for(int j = 0; j < n; j++){ if(i != j){ for(int k = i + 1; k <= n; k++){ B[j][k] -= B[i][k] * B[j][i]; } } } } vector res(n); for(int i = 0; i < n; i++){ res[i] = B[i][n]; } return res; } template mat pow(mat A, long long cnt) { if(A.row() != A.column()){ cout << "累乗不可" << endl; } int n = A.row(); mat B(n, n); for(int i = 0; i < n; i++){ B[i][i] = 1; } while(cnt > 0){ if(cnt & 1) B = B * A; A = A * A; cnt >>= 1; } return B; } using mod = ModInt; // 宣言 mat A(n, m); int main(){ mat P(6,6); P[0][2] = 1; P[1][3] = 1; P[2][4] = 1; P[3][5] = 1; P[4][2] = 1; P[4][4] = 1; P[5][2] = 1; P[5][3] = 1; P[5][4] = 2; P[5][5] = 1; mat x(6,1); x[0][0] = 1; x[1][0] = 1; x[2][0] = 1; x[3][0] = 3; x[4][0] = 2; x[5][0] = 7; ll n; cin >> n; if(n<=5){ cout << x[n][0] << endl; return 0; } auto X = pow(P,(n-4)/2); x = X*x; if(n%2==0){ cout << x[4][0] << endl; }else{ cout << x[5][0] << endl; } return 0; }