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.

Examples

Input

3


Output

4


Input

6


Output

30


Input

1000


Output

972926972
#include<iostream>
using namespace std;
int main(){
	int n,s[1100];
	cin>>n;
	int tmp;
  	for(int i=0;i<=n;i++) s[i]=0;
	for(int i=2;i<=n;++i){
		tmp=i;
		for(int j=2;j<=n;++j){
			if(tmp==0) break;
			while(tmp%j==0){
				tmp/=j;
				++s[j];
			}
		}
	}
	long long cnt=1;
	for(int i=2;i<=n;++i) cnt=cnt*(s[i]+1)%1000000007;
	cout<<cnt<<endl;
	return 0;
}