Find the remainder by dividing the number of positive divisors of $ N! $ By $ 10 ^ 9 + 7 $ when the integer $ N $ is given.
Let the prime factors of $ N! $ Be {$ p_0, p_1, ..., p_k
Therefore, the number of divisors of $ N! $ Is
From the above, it can be seen that the number of divisors can be obtained by finding the number of each prime factor of $ N! $.
Here, in order to count the number of each prime factor, $ (Number of prime factors p included in N!) = \ Sigma_ {k = 1} ^ {\ infinty} \ left \ [\ frac {n} {p ^ k} \ right ] = \ left \ [\ frac {n} {p ^ 1} \ right ] + \ left \ [\ frac {n} {p ^ 2} \ right ] + ... $ (Details of this theorem here).
import math
N = math.factorial(int(input()))
res = 1
p = 2 #Factors to check
# p<=sqrt(N)It is enough to investigate the factors that satisfy
while p*p <= N:
i = 1
# p^k(k=1~)Count the number of multiples of and add them together
while(N % p == 0):
i += 1
N //= p
# N!The number of divisors of is i_0*i_1*...*i_k
res *= i
p += 1
if(N != 1):
res *= 2
print(res % (10**9+7))