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 <vector>

using namespace std;

int main(){
    int n; cin >> n;
    vector<int> ps(n+1, 1);
    for(int i=2; i<=n; ++i){
        int t=i;
        for(int j=2; j<=i; ++j){
            while(t%j==0){
                t/=j;
                ++ps[j];
            }
        }
    }
    long long ans=1;
    for(int i=0; i<=n; ++i){
        ans=(long long)ans*(long long)ps[i]%(1000*1000*1000+7);
    }
    cout << ans << endl;
    return 0;
}
