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)

#![allow(dead_code, unused_imports, non_snake_case)]

use std::io::*;
use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::str::FromStr;

const MOD: i32 = 1_000_000_007;

fn main() {
    let n: u64 = input();
    let mut m = HashMap::new();

    for i in 1..n + 1 {
        let mut x = i;
        let mut div: u64 = 2;
        loop {
            if x % div == 0 {
                x /= div;
                *m.entry(div).or_insert(0) += 1;
                continue;
            }
            div += 1;
            if div > x {
                break
            }
        }
    }
    let mut ans: u64 = 1;
    for &val in m.values() {
        ans = ans * (val + 1) % 1_000_000_007;
    }
    println!("{}", ans);
}

trait Read {
    fn read(s: &str) -> Self;
}

fn input<T: Read>() -> T {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    T::read(buf.trim_right())
}

macro_rules! read_impl {
    ($($t:ty)*) => ($(
        impl Read for $t {
            fn read(s: &str) -> $t{
                s.parse().unwrap()
            }
        }
    )*)
}
read_impl! { usize u8 u16 u32 u64 isize i8 i16 i32 i64 f32 f64 }

impl Read for String {
    fn read(s: &str) -> Self {
        s.to_string()
    }
}

impl Read for Vec<char> {
    fn read(s: &str) -> Self {
        s.chars().collect()
    }
}

impl<T: Read> Read for Vec<T> {
    fn read(s: &str) -> Self {
        s.split_whitespace().map(T::read).collect()
    }
}

impl<A: Read, B: Read> Read for (A, B) {
    fn read(s: &str) -> Self {
        let tokens: Vec<_> = s.split_whitespace().collect();
        (A::read(tokens[0]), B::read(tokens[1]))
    }
}

impl<A: Read, B: Read, C: Read> Read for (A, B, C) {
    fn read(s: &str) -> Self {
        let tokens: Vec<_> = s.split_whitespace().collect();
        (A::read(tokens[0]), B::read(tokens[1]), C::read(tokens[2]))
    }
}

impl<A: Read, B: Read, C: Read, D: Read> Read for (A, B, C, D) {
    fn read(s: &str) -> Self {
        let tokens: Vec<_> = s.split_whitespace().collect();
        (A::read(tokens[0]), B::read(tokens[1]), C::read(tokens[2]), D::read(tokens[3]))
    }
}