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;
const int MOD = 1e9 + 7;
typedef long long ll;

int main() {
  int n;
  cin >> n;
  unordered_map<int, int> mp;

  for (int i = 2; i <= n; ++i) {
    int t = i;
    int j = 2;
    while (t != 1) {
      if (t % j == 0)
        t /= j, mp[j]++;
      else
        j++;
    }
  }

  ll ans = 1;
  for (auto m : mp) ans = ans * (m.second + 1) % MOD;

  cout << ans << endl;
}
