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 ll mod = 1e9+7;

int main()
{
  int N; cin >> N;

  map<int, ll> prime_factor_cnt;
  for (int i = 2; i <= N; ++i) {

    int k = i;
    for (int j = 2; k > 1;) {
      if (k % j == 0) {
        prime_factor_cnt[j]++;
        k /= j;
      } else {
        j++;
      }
    }
  }

  ll ans = 1;
  for (auto v : prime_factor_cnt) {
    ans = ans*(v.second+1)%mod;
  }

  cout << ans << endl;
}