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>
#include <algorithm>
using namespace std;
int so[1001];

int main(void){
    for(int i=2;i*i<=1000;i++){
        if(so[i]!=1){
            for(int j=i*2;j<=1000;j+=i)so[j]=1;
        }
    }
    long long n,ans=1;
    cin>>n;
    for(int i=2;i<=n;i++){
        if(so[i])continue;
        int j=i,ct=0;
        while(n>=j){
            ct+=(n/j);
            j*=i;
        }
        ans=(ans*(ct+1))%1000000007;
        
    }
    cout<<ans<<endl;
}
