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 (2.7.6) (judge verdict: Accepted)

N = input()
mod = 10 ** 9 + 7
num_p = [1] * 1001
p = []
# find p
for i in range(2, N + 1):
  canDivide = True
  for j in range(2, i):
    if i % j == 0:
      canDivide = False
      break
  if canDivide:
    p.append(i)

# factorization
for i in range(2, N + 1):
  for j in p:
    c = 0
    while i % j == 0:
      c += 1
      i /= j
    num_p[j] = (num_p[j] + c) % mod

print reduce(lambda x, y: x * y, num_p) % mod