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: Runtime Error)

from functools import reduce
from copy import deepcopy

n = int(input())

def dadd(t, s): 
    for k,v in s.items():
        t[k] = t.get(k, 0) + v 
    return t

def pfd(c, i): 
    for j in range(2, i // 2 + 1): 
        if i % j == 0:
            d = i // j
            return dadd(deepcopy(c[j]), c.get(d, dict()))
    return { i: 1 } 

p,c = {},{}
for i in range(2, n + 1): 
    q = pfd(c, i)
    c[i] = q 
    dadd(p, q)

tot = reduce(lambda a,(k,v): a * (v + 1), p.items(), 1)
print(tot % (10 ** 9 + 7))