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<string>
#include<vector>
#include<algorithm>

using namespace std;

int N;
vector<long> p(1001,1);
int main(){
    cin >> N;
    long long ans=1,bikkuri=1;
    int i,j,k;
    for(i=2;i<=N;i++){
        int n=i;
        for(j=2;j<=i;j++){
            while(n%j==0){
                p[j]++;
                n=n/j;
            }
        }
    }
    for(i=0;i<=N;i++) {
        ans =ans*p[i]%(1000000000+7);
    }
    cout << ans;
}