Problem:
Score : 300 points

Problem Statement

You are given an integer N.
Find the number of the positive divisors of N!, modulo 10^9+7.

Constraints

1≤N≤10^3

Input

The input is given from Standard Input in the following format:

N

Output

Print the number of the positive divisors of N!, modulo 10^9+7.

Sample Input 1

3

Sample Output 1

4

There are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972

Solution in Python (3.4.3) (judge verdict: Accepted)

MOD = 10**9+7
def factorize(N):
    n = N
    fact = []
    for i in range(2,int(N**0.5)+1): # intに変換すること
        while(n%i==0):
            n //= i #  整数除算(//)を使うこと
            fact.append(i)
    if n!=1:
        fact.append(n)
    return fact
N = int(input())
cnt = [0] * (N+1)
for n in range(1,N+1):
    fact = factorize(n)
    for f in fact:
        cnt[f] += 1

ans = 1
for n in range(N+1):
    ans *= (cnt[n]+1)
    ans %= MOD
print (ans)