#pragma region template 2.4 #include using namespace std; template using pq_asc = priority_queue, greater>; typedef long long ll; typedef vector vi; typedef vector vvi; typedef pair ii; typedef vector vii; typedef vector vs; #define REP(i, n) for (ll i = 0; i < (n); ++i) #define REP1(i, n) for (ll i = 1; i <= (n); ++i) #define FOR(i, a) for (auto &i : a) #define CH(f, x, y) x = f(x, y) #define IN(T, x) \ T x; \ cin >> x; #define AIN(T, a, n) \ vector a(n); \ FOR(i, a) \ cin >> i; #define A2IN(T1, a, T2, b, n) \ vector a(n); \ vector b(n); \ REP(i, n) \ cin >> a[i] >> b[i]; #define OUT(x) cout << (x) << endl; #define FOUT(x) cout << fixed << setprecision(15) << (x) << endl; #define ALL(a) (a).begin(), (a).end() #define SORT(a) sort(ALL(a)) #define RSORT(a) \ SORT(a); \ reverse(ALL(a)) #define DUMP(x) cout << #x << " = " << (x) << endl; #define DUMPA(a) \ cout << #a << " = {"; \ JOUT(ALL(a), ", ", cout) << "}" << endl; template ostream &JOUT(T s, T e, string sep = " ", ostream &os = cout) { if (s != e) { os << *s; ++s; } while (s != e) { os << sep << *s; ++s; } return os; } ostream &YES(bool cond, string yes = "Yes", string no = "No", ostream &os = cout) { if (cond) { os << yes << endl; } else { os << no << endl; } return os; } template ostream &operator<<(ostream &os, const pair &p) { os << '(' << p.first << ", " << p.second << ')'; return os; } template ostream &operator<<(ostream &os, const vector &v) { os << '['; JOUT(ALL(v), ", ", os) << ']'; return os; } const ll INF = 1e18; const ll MOD = 1e9 + 7; #pragma endregion template #pragma region mint 1.1 struct mint { ll a; mint(ll a = 0) : a((a % MOD + MOD) % MOD) {} mint pow(ll y) { ll exp = y; mint res = 1; mint p = a; while (exp) { if (exp & 1) { res *= p; } exp >>= 1; p *= p; } return res; } mint pow(mint y) { return pow(y.a); } mint &operator+=(ll y) { *this = a + y; return *this; } mint &operator+=(mint y) { *this += y.a; return *this; } mint &operator-=(ll y) { *this = a - y; return *this; } mint &operator-=(mint y) { *this -= y.a; return *this; } mint &operator*=(ll y) { *this = a * y; return *this; } mint &operator*=(mint y) { *this *= y.a; return *this; } mint &operator/=(ll y) { *this *= mint(y).pow(MOD - 2); return *this; } mint &operator/=(const mint y) { *this /= y.a; return *this; } mint &operator++() { *this += 1; return *this; } mint &operator++(int) { *this += 1; return *this; } mint &operator--() { *this -= 1; return *this; } mint &operator--(int) { *this -= 1; return *this; } }; mint operator+(const mint &x, const mint &y) { return mint(x.a) += y; } mint operator+(const mint &x, const ll &y) { return mint(x.a) += y; } mint operator+(const ll &x, mint &y) { return mint(x) += y; } mint operator-(const mint &x, const mint &y) { return mint(x.a) -= y; } mint operator-(const mint &x, const ll &y) { return mint(x.a) -= y; } mint operator-(const ll &x, const mint &y) { return mint(x) -= y; } mint operator*(const mint &x, const mint &y) { return mint(x.a) *= y; } mint operator*(const mint &x, const ll &y) { return mint(x.a) *= y; } mint operator*(const ll &x, const mint &y) { return mint(x) *= y; } mint operator/(const mint &x, const mint &y) { return mint(x.a) /= y; } mint operator/(const mint &x, const ll &y) { return mint(x.a) /= y; } mint operator/(const ll &x, const mint &y) { return mint(x) /= y; } bool operator==(const mint &x, const mint &y) { return x.a == y.a; } bool operator==(const mint &x, const ll &y) { return x.a == y; } bool operator==(const ll &x, mint &y) { return x == y.a; } bool operator!=(const mint &x, const mint &y) { return !(x == y); } bool operator!=(const mint &x, const ll &y) { return !(x == y); } bool operator!=(const ll &x, mint &y) { return !(x == y); } istream &operator>>(istream &is, mint &i) { is >> i.a; return is; } ostream &operator<<(ostream &os, const mint &i) { os << i.a; return os; } typedef vector vm; #pragma endregion mint #pragma region matrix 1.0 template struct matrix { ll n, m; vector> A; matrix() {} matrix(ll n) : n(n), m(n) { A.assign(n, vector(n)); } matrix(ll n, ll m) : n(n), m(m) { A.assign(n, vector(m)); } matrix(vector> X) : A(X) { n = X.size(); m = X[0].size(); } matrix pow(ll k) { matrix res = matrix(n, n); REP(i, n) { res[i][i] = 1; } matrix P = A; while (k) { if (k & 1) { res *= P; } k >>= 1; P *= P; } return res; } matrix &operator+=(matrix B) { REP(i, n) { REP(j, m) { A[i][j] += B[i][j]; } } return *this; } matrix &operator-=(matrix B) { REP(i, n) { REP(j, m) { A[i][j] -= B[i][j]; } } return *this; } matrix &operator*=(T x) { REP(i, n) { REP(j, m) { A[i][j] *= x; } } return *this; } matrix &operator*=(matrix B) { vector> X(n, vector(m)); REP(i, n) { REP(j, B.m) { REP(k, m) { X[i][j] += A[i][k] * B[k][j]; } } } A = X; return *this; } matrix &operator/=(T x) { REP(i, n) { REP(j, m) { A[i][j] /= x; } } return *this; } vector &operator[](int i) { return A[i]; } }; template matrix operator+(const matrix &A, const matrix &B) { return matrix(A.A) += B; } template matrix operator-(const matrix &A, const matrix &B) { return matrix(A.A) -= B; } template matrix operator*(const matrix &A, const T &x) { return matrix(A.A) *= x; } template matrix operator*(const T &x, const matrix &A) { return matrix(A.A) *= x; } template matrix operator*(const matrix &A, const matrix &B) { return matrix(A.A) *= B; } template matrix operator/(const matrix &A, const T &x) { return matrix(A.A) /= x; } template bool operator==(const matrix &x, const matrix &y) { return x.A == y.A; } template bool operator!=(const matrix &x, const matrix &y) { return x.A != y.A; } #pragma endregion matrix int main() { IN(ll, N); vm p(7); p[0] = 1; REP1(i, 6) { REP(j, i) { p[i] += p[j] / 6; } } if (N <= 6) { OUT(p[N]); } else { matrix P(6); REP(i, 6) { P[0][i] = mint(1) / 6; } REP(i, 5) { P[i + 1][i] = 1; } mint ans = 0; auto Q = P.pow(N - 6); REP(i, 6) { ans += Q[0][i] * p[6 - i]; } OUT(ans); } }