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 <vector>
#include <set>
#include <algorithm>
#include <math.h>
#include <string.h>
#include <map>
using namespace std;

int main()
{
  int n;
  cin>>n;
  long long int ans=1;
  map<int, int> mp;
  for(int i=2;i<=n;i++){
    int tmp=i;
    for(int j=2;j<=i;j++){
      while(tmp%j==0){
        tmp/=j;
	mp[j]++;
      }
    }
  }
  for (auto x : mp){
    ans = ans*(x.second+1);
    ans = ans%(1000000007);
  }
  cout<< ans <<endl;
}
