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;

int main() {
  int N, mod = 1e9+7;
  cin >> N;
  vector<int> V(N + 1);
  for (int i = 2; i <= N; i++) {
    int tmp = i;
    for (int j = 2; j <= N; j++) {
      while (tmp % j == 0) tmp /= j, V.at(j)++;
    }
  }
  long ans = 1;
  for (int i = 2; i < N + 1; i++) {
    if (V.at(i)) (ans *= V.at(i) + 1) %= mod;
  }
  cout << ans << "\n";
}