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 <cstdio>
int factor[1001];
const int MOD = 1e9 + 7;

void factorize(int N) {
  for (int i = 2; i * i <= N; ++i) {
    while (N % i == 0) {
      factor[i]++;
      N /= i;
    }
  }
  if (N != 1)
    factor[N]++;
}
int main() {
  int N;
  scanf("%d", &N);
  for (int i = 1; i <= N; ++i)
    factorize(i);
  int ans = 1;
  for (int i = 2; i <= N; ++i)
    ans = 1LL * ans * (1 + factor[i]) % MOD;
  printf("%d\n", ans);
  return 0;
}
