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<map>
#include<cstdio>

int main(){
    int n;
    scanf("%d", &n);

    long long ans = 1;
    const long long mod = 1e9 + 7;

    std::map<int, long long> factors;
    for(int i = 2; i <= n; i++){
        for(int j = 2, d = i; d > 1; j++){
            while(d % j == 0){
                factors[j]++;
                d /= j;
            }
        }
    }

    for(auto p : factors) ans = ans *(1 + p.second) % mod;
    printf("%ld\n", ans);
    return 0;
}