Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3

Sample Output 1

4

There are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972

Solution in Rust (1.15.1) (judge verdict: Accepted)

fn rec(x: usize, v: &mut Vec<usize>) {
    if x == 1 {
        return;
    }

    let div = (2..(x as f64).sqrt() as usize + 1)
        .find(|i| x % i == 0)
        .unwrap_or(x);
    v[div] += 1;
    rec(x / div, v);
}

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).ok();
    let n: usize = buf.trim().parse().unwrap();
    let mut v = vec![0_usize; n + 1];
    for i in 2..n + 1 {
        rec(i, &mut v);
    }

    let mut ans = 1;
    for &i in v.iter() {
        ans *= i + 1;
        ans %= 1_000_000_007;
    }
    println!("{}", ans);
}