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>
#define ppp 1000000007
using namespace std;
int main(){
int n,i,ic,j;
long long int a[1000]={0},s=1;
cin>>n;
for(i=2;i<=n;i++){
ic=i;
for(j=2;j<=ic;j++){
if(ic%j==0){
a[j]++;
ic/=j;
j--;}
}
}
for(i=2;i<=n;i++){
s*=(a[i]+1);
if(s>=ppp){
s%=ppp;
}
}
cout<<s;
return 0;
}
