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 <bits/stdc++.h>
using namespace std;
typedef long long ll;

int main() {
    int n;cin>>n;
    map<int,int> pf;
    for (int i=2;i<=n;i++) {
        int t=i;
        for (int j=2;j<=t;j++)
            while (t%j==0) {
                pf[j]++;
                t/=j;
            }
    }
    ll ans=1;
    for (auto p:pf)
        ans=ans*(p.second+1)%1000000007;
    cout<<ans<<endl;
    return 0;
}