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 <bits/stdc++.h>
using namespace std;
typedef long long ll;

ll MOD = 1e9 + 7;

int d[1001];

int main() {
  int N;
  cin >> N;
  ll ans = 1;
  for (int i = 2; i <= N; i++) {
    int M = i;
    for (int j = 2; j <= N; j++) {
      while (M % j == 0) {
        M /= j;
        d[j]++;
      }
    }
  }
  for (int i = 2; i <= N; i++) {
    ans = ans * (d[i] + 1) % MOD;
  }
  cout << ans << endl;
}
