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