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;
using ll = long long;

const int MOD = (int)1e9 + 7;

int main() {
  int n;
  cin >> n;
  map<int, int> m;
  for (int i = 1; i <= n; i++) {
    int x = i;
    for (int j = 2; j * j <= x; j++)
      while (x % j == 0) {
        m[j]++;
        x /= j;
      }
    if (x > 1) m[x]++;
  }
  ll ans = 1;
  for (auto it : m) ans = (ans * (it.second + 1)) % MOD;
  cout << ans << endl;
}
