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(unused_mut)]
#![allow(non_snake_case)]
#![allow(unused_macros)]
#![allow(unused_variables)]
#![allow(unused_imports)]
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

macro_rules! max {
    ($x: expr) => ($x);
    ($x: expr, $($y: expr),+) => {
        ::std::cmp::max($x, max!($($y),+))
    };
}

macro_rules! min {
    ($x: expr) => ($x);
    ($x: expr, $($y: expr),+) => {
        ::std::cmp::min($x, max!($($y),+))
    };
}

const MOD: usize = 1_000_000_007;
const MAX: usize = 1_000;
use std::cmp;
use std::collections::{HashSet, BinaryHeap, VecDeque};
use std::iter::FromIterator;
fn main() {
    input!{
        N: usize,
    }
    if N == 1 {
        println!("1");
        return;
    }

    let mut is_prime = [true; MAX+1];
    for p in 2.. {
        if p*p > MAX { break; }
        else if is_prime[p] {
            let mut nop = p*p;
            while nop <= MAX {
                is_prime[nop] = false;
                nop += p;
            }
        }
    }

    let mut prime_count = [0; MAX+1];
    for n in 2..N+1 {
        for ((p, _), c) in (0..n+1)
        .zip(is_prime.iter()).zip(prime_count.iter_mut())
        .skip(2).filter(|x| *(x.0).1)
        {
            let mut count = 0;
            let mut res = n;
            while res % p == 0 {
                count += 1;
                res /= p;
            }
            *c += count;
        }
    }
    let ans = prime_count.iter().fold(1, |acc, &c| (acc*(c+1)) % MOD);
    println!("{}", ans);
}