#include #define fi first #define se second #define rep(i,s,n) for (int i = (s); i < (n); ++i) #define rrep(i,n,g) for (int i = (n)-1; i >= (g); --i) #define all(a) a.begin(),a.end() #define rall(a) a.rbegin(),a.rend() #define len(x) (int)(x).size() #define dup(x,y) (((x)+(y)-1)/(y)) #define pb push_back #define eb emplace_back #define Field(T) vector> using namespace std; using ll = long long; using ull = unsigned long long; template using pq = priority_queue,greater>; using P = pair; templatebool chmax(T&a,T b){if(abool chmin(T&a,T b){if(b struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { assert(x); int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; using i64 = long long; static inline i64 my_div(i64 n, i64 p) { return double(n) / p; }; __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) i64 prime_counting(i64 N) { i64 N2 = sqrt(N); i64 NdN2 = my_div(N, N2); vector hl(NdN2); for (int i = 1; i < NdN2; i++) hl[i] = my_div(N, i) - 1; vector hs(N2 + 1); iota(begin(hs), end(hs), -1); for (int x = 2, pi = 0; x <= N2; ++x) { if (hs[x] == hs[x - 1]) continue; i64 x2 = i64(x) * x; i64 imax = min(NdN2, my_div(N, x2) + 1); i64 ix = x; for (i64 i = 1; i < imax; ++i) { hl[i] -= (ix < NdN2 ? hl[ix] : hs[my_div(N, ix)]) - pi; ix += x; } for (int n = N2; n >= x2; n--) { hs[n] -= hs[my_div(n, x)] - pi; } ++pi; } return hl[1]; } using mint = ModInt<1000000007>; int main() { ll n; cin >> n; ll s = sqrt(n)+300000; mint ans = 1; if (s < n) { ll k = prime_counting(n); rep(cnt,2,s) { ll nk = prime_counting(max(n/cnt, s)); ans *= mint(cnt).pow(k-nk); if (n/cnt <= s) break; k = nk; } } vector p(s+1, 1); p[0] = p[1] = 0; rep(i,2,s+1) { if (p[i]) { for (int j = i*2; j <= s; j += i) p[j] = 0; } } rep(i,0,min(s+1, n+1)) if (p[i]) { mint b = 1; ll x = n; while(x > 0) { x /= i; b += x; } ans *= b; } cout << ans << endl; return 0; }