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;

void f(int n, map<int, int>& M) {
  int x = 2;
  for (int x = 2; x * x <= n; x++) {
    while (n % x == 0) {
      n /= x;
      M[x]++;
    }
  }
  if (n != 1) M[n]++;
}

int main() {
  int N, NN = 1000000007;
  cin >> N;
  map<int, int> M;
  for (int n = 2; n <= N; n++) {
    f(n, M);
  }
  long ans = 1;
  for (auto m : M) {
    ans = ans * (m.second+1) % NN;
  }
  cout << ans << endl;
}