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 <cmath>
#include <algorithm>
#define MOD 1000000007
using namespace std;
typedef long long ll;
 
int main(){
 
int n;
cin >> n;
 
int d[1010] = {0};
for(int i = 2; i <= n; i++){
int num = i;
 for(int j = 2; j <= n; j++){
  while(num % j == 0){
   d[j]++;
   num /= j;
  }
 }
}
 
ll ans = 1;
 
for(int i = 0; i <= n; i++){
ans *= (d[i] + 1);
ans %= MOD;
}
 
cout << ans << endl;
 
return 0;
}