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;

map<long, int> pf(long n) {
  map<long, int> ma;
  for (long i = 2; i * i <= n; i++) {
    while (n % i == 0) ma[i]++, n /= i;
  }
  if (n != 1) ma[n]++;
  return ma;
}

int main() {
  int N, M = 1e9+7;
  cin >> N;
  vector<int> cnt(N + 1);
  for (int i = 1; i <= N; i++) {
    for (auto [a, b] : pf(i)) cnt.at(a) += b;
  }
  long ans = 1;
  for (auto c : cnt) {
    ans *= ++c;
    ans %= M;
  }
  cout << ans << "\n";
}