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 Ruby (2.3.3) (judge verdict: Accepted)

# Your code here!
n=gets.to_i


array=[2,3,5,7,11,13,17,19,23,29,31]
array2=[0,0,0,0,0,0,0,0,0,0,0]
array3=[[2,0],[3,0],[5,0],[7,0],[11,0],[13,0],[17,0],[19,0],[23,0],[29,0],[31,0]]


j=1
k=j+1
n.times{

loop{
    i=0
11.times{
    if j%array[i]==0
        j=j/array[i]
        array3[i][1]+=1
        break
    
 else
        i+=1
    end
    
    
    
}
if j==1 
    break
end

if  i==11 && array3.flatten.include?(j)
    nnn=array3.flatten.index(j)
    array3[nnn/2][1]+=1
    break
elsif  i==11
   array3<<[j,1]
   break
end


}


j=k
k=k+1


}





answer=1
kk=0
array3.length.times{
    answer=answer*(array3[kk][1]+1)
    answer=answer%1000000007
    kk+=1
}


puts answer