import sys read = sys.stdin.buffer.read readline = sys.stdin.buffer.readline readlines = sys.stdin.buffer.readlines import numpy as np from functools import lru_cache MOD = 10 ** 9 + 7 U = 10 ** 3 + 10 is_prime = np.zeros(U, np.bool) is_prime[2] = 1 is_prime[3::2] = 1 for p in range(3, U, 2): if p * p >= U: break if is_prime[p]: is_prime[p * p:: p + p] = 0 primes = np.where(is_prime)[0] def cumprod(A, MOD=MOD): L = len(A) Lsq = int(L**.5 + 1) A = np.resize(A, Lsq**2).reshape(Lsq, Lsq) for n in range(1, Lsq): A[:, n] *= A[:, n - 1] A[:, n] %= MOD for n in range(1, Lsq): A[n] *= A[n - 1, -1] A[n] %= MOD return A.ravel()[:L] def make_fact(U, MOD=MOD): x = np.arange(U, dtype=np.int64) x[0] = 1 fact = cumprod(x, MOD) fact.flags.writeable = False return fact def factor(M): pf = primes[M % primes == 0] for p in pf: e = 0 while M % p == 0: M //= p e += 1 yield (int(p), e) if M > 1: yield (int(M), 1) @lru_cache(None) def GL(p, n): # count the element of GL(n,F_p) x = 1 for i in range(n): x *= (p ** n - p ** i) x %= MOD return x % MOD def Aut(p, e, partition): # count Aut(prod Z/p^{n_i}) x = 1 for i in range(1, e + 1): n = sum(k == i for k in partition) x *= GL(p, n) x *= pow(p, (i - 1) * n, MOD) return x % MOD def make_partitions(N, largest=None): if N == 0: yield [] return if largest is None: largest = N if largest > N: largest = N for i in range(largest, 0, -1): for p in make_partitions(N - i, i): yield p + [i] def compute_p_part(p, e): # sum(1 / Aut) x = 0 for par in make_partitions(e): aut = Aut(p, e, par) x += pow(aut, MOD - 2, MOD) x %= MOD return x def solve(M): fact = make_fact(M + 10) x = 1 for p, e in factor(M): x *= compute_p_part(p, e) x %= MOD x *= fact[M] return x % MOD M = int(read()) print(solve(M))