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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

Var i,n,j,rem,fin:Longint;
    a:Array[1 .. 10000] of Longint;
Begin
    Readln(n);
    Fillchar(a,sizeof(a),0);
    fin:=1;
    For i:=1 to n do begin
        rem:=i;
        For j:=2 to rem do
            While rem mod j = 0 do begin
                Inc(a[j]);
                rem:=rem div j;
            End;
    End;
    For i:=1 to n do fin:=fin*(a[i]+1) mod 1000000007;
    Writeln(fin);
End.