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;

long long n;
long long cnt[1005] = {0}, ans = 1;

int main() {
  cin >> n;
  for(long long i = 2; i <= n; ++i) {
    long long now = i;
    for(long long j = 2; j <= now; ++j)
      while(now > 0 && now % j == 0) {
        ++cnt[j];
        now /= j;
      }
  }
  for(long long i = 0; i <= n; ++i)
    if(cnt[i] != 0) {
      ans *= cnt[i] + 1;
      ans %= 1000000007;
    }
  cout << ans << endl;
  return 0;
}