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<map>
using namespace std;
typedef long long ll;
const ll mod = 1e9 + 7;

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