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>

using namespace std;
using ll = long long;
int main (void){
    ll n;
    cin >> n;
    ll num[n];
    for(ll i=0;i<n;i++)num[i]=1;
    ll ans=1;
    ll i,j,k;
    for(i=2;i <= n;i++){
        ll tmp=i;
        for(j=2;i>=j;j++){
            for(k=0;tmp%j==0;k++){
                tmp/=j;
            }
            num[j-1]+=k;
        }
    }

    for(i=0;i<n;i++){
        ans*=num[i];
        ans%=1000000007;
    }

    cout << ans << endl;
}
