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>
using namespace std;
#define MOD 1000000007
#define NMAX 1000

int main() {
  int n;
  cin >> n;
  vector<int> a(NMAX+1, 1);
  for (int i = 2; i <= n; i++) {
    int p = i;
    for (int j = 2; j*j <= i; j++) {
      if (p % j == 0) {
        p /= j;
        a[j]++;
        j--;
      }
    }
    a[p]++;
  }
  int ans = 1;
  for (int i = 2; i <= n; i++) {
    ans = 1LL * ans * a[i] % MOD;
  }
  cout << ans << endl;
}