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;
int main() {
int N;  
cin >> N; 
int A[1010] = {}; 
long long int B[1010] = {}; 
for(int i = 1; i <= N; i++) {
A[i] = i; 
B[i] = 1; 
}
for (int j = 2; j <= N; j++) {
  for (int i = 1; i <= N; i++) {
    while(A[i] % j == 0){
B[j] ++; 
A[i] /= j; 
}
}
}
long long int ans = 1; 
long long int P = 1e9 + 7; 
for(int i = 1; i <= N; i++) {
ans = (ans * B[i]) % P; 
}
cout << ans << endl; 
}