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())
fact=1
for i in range(2,n+1):
	fact*=i
sieve=[0]*2+[1]*100000
primes=[]
for i,e in enumerate(sieve):
	if sieve[i]==1:
		primes.append(i)
		for j in range(i*2,len(sieve),i):
			sieve[j]=0
ans=1
MOD=10**9+7
for prime in primes:
	if fact%prime==0:
		count=0
		while fact%prime==0:
			fact=fact//prime
			count+=1
		ans=(ans*(count+1))%MOD
print(ans%MOD)