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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <string>
#include <algorithm>
#include <cmath>
using namespace std;
int main(){
	long long n;
	cin>>n;
	int c[1000];
	int now;
	for(int i=0;i<1000;i++)c[i]=1;
	for(int i=2;i<=n;i++){
		now=i;
		for(int j=2;j<=i;j++){
			if(now%j==0){
				c[j-1]++;
				now/=j;
				j--;
			}
		}
	}
	long long ans=1;
	for(int i=0;i<1000;i++)ans=ans*c[i]%1000000007;
	cout<<ans%1000000007<<endl;
	return 0;
}