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)

N=int(input())
M=[0]*1001

for i in range(2,N+1):
  j=2
  ii=i
  while 1:
    #print(ii)
    if ii%j==0:
      M[j]+=1
      ii//=j
      j=2
    else:
      j+=1
    if ii==1:
      #print("")
      break
#print(M[:10])

ans=1
for m in M:
  if m:
    ans*=(m+1)
print(ans%(10**9+7))