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)

#[macro_use]
mod input {

use std;
use std::io;

const SPLIT_DELIMITER: char = ' ';

#[macro_export]
#[allow(unused_macros)]
macro_rules! input {
    ( $($x:expr ),*) => {
        {
            let temp_str = input_line_str();
            let mut split_result_iter = temp_str.split_whitespace();
                $(
                let buf_split_result = split_result_iter.next();
                let buf_split_result = buf_split_result.unwrap();
                    ($x) = buf_split_result.parse().unwrap();
                )*
        }
    };
}

#[allow(dead_code)]
pub fn input_line_str() -> String {
    let mut s = String::new();
    io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

#[allow(dead_code)]
pub fn p<T>(t: T)
where
    T: std::fmt::Display,
{
    println!("{}", t);
}

#[allow(dead_code)]
pub fn input_vector2d<T>(line: usize) -> Vec<Vec<T>>
where
    T: std::str::FromStr,
{
    let mut v: Vec<Vec<T>> = Vec::new();

    for _ in 0..line {
        let vec_line = input_vector();
        v.push(vec_line);
    }
    v
}

#[allow(dead_code)]
pub fn input_vector<T>() -> Vec<T>
where
    T: std::str::FromStr,
{
    let mut v: Vec<T> = Vec::new();

    let s = input_line_str();
    let split_result = s.split(SPLIT_DELIMITER);
    for z in split_result {
        let buf = match z.parse() {
            Ok(r) => r,
            Err(_) => panic!("Parse Error"),
        };
        v.push(buf);
    }
    v
}

#[allow(dead_code)]
pub fn str2vec(s: &str) -> Vec<char> {
    let mut v: Vec<char> = Vec::new();
    for c in s.chars() {
        v.push(c);
    }
    v
}
}
mod modint {

use std;
use std::fmt;
use std::num::ParseIntError;
use std::ops;
use std::str::FromStr;

#[derive(PartialEq, Eq, Debug, Clone)]
pub struct Modint {
    p: usize,
    v: usize,
}

const DEFAULT_MODNUM: usize = 1_000_000_007;

impl Modint {
    #[allow(dead_code)]
    pub fn new(p: usize) -> Modint {
        Modint { p: p, v: 0 }
    }
    #[allow(dead_code)]
    pub fn from(p: usize, v: usize) -> Modint {
        Modint { p: p, v: v % p }
    }
}

impl FromStr for Modint {
    type Err = ParseIntError;

    fn from_str(s: &str) -> Result<Self, Self::Err> {
        let num: usize;
        num = s.parse()?;
        Ok(Modint {
            p: DEFAULT_MODNUM,
            v: num,
        })
    }
}

impl fmt::Display for Modint {
    fn fmt<'a>(&self, f: &mut fmt::Formatter<'a>) -> fmt::Result {
        write!(f, "{}", self.v)
    }
}

impl<'a> ops::Add for &'a Modint {
    type Output = Modint;

    #[allow(dead_code)]
    fn add(self, other: &'a Modint) -> Modint {
        if self.p != other.p {
            panic!("Mod Error");
        }
        Modint {
            p: self.p,
            v: (self.v + other.v) % self.p,
        }
    }
}

impl<'a> ops::Sub for &'a Modint {
    type Output = Modint;

    #[allow(dead_code)]
    fn sub(self, other: &'a Modint) -> Modint {
        if self.p != other.p {
            panic!("Mod Error");
        }
        Modint {
            p: self.p,
            v: (self.v + self.p - (other.v % self.p)) % self.p,
        }
    }
}

impl<'a> ops::Mul for &'a Modint {
    type Output = Modint;

    #[allow(dead_code)]
    fn mul(self, other: &'a Modint) -> Modint {
        if self.p != other.p {
            panic!("Mod Error");
        }
        Modint {
            p: self.p,
            v: (self.v * other.v) % self.p,
        }
    }
}

impl<'a> ops::Div for &'a Modint {
    type Output = Modint;

    fn div(self, other: &'a Modint) -> Modint {
        if self.p != other.p {
            panic!("Mod Error");
        }
        let mut obj = self.clone();
        obj.div_uint(other.v);
        obj
    }
}

impl Modint {
    #[allow(dead_code)]
    pub fn add_uint(&mut self, n: usize) -> &Self {
        self.v += n;
        self.v %= self.p;
        self
    }

    #[allow(dead_code)]
    pub fn sub_uint(&mut self, mut n: usize) -> &Self {
        n = n % self.p;
        self.v += self.p;
        self.v -= n;
        self.v %= self.p;
        self
    }

    #[allow(dead_code)]
    pub fn mul_uint(&mut self, n: usize) -> &Self {
        self.v *= n;
        self.v %= self.p;
        self
    }

    #[allow(dead_code)]
    pub fn div_uint(&mut self, n: usize) -> &Self {
        let mut obj = Modint::from(self.p, n);
        obj.inv();
        self.v *= obj.v;
        self.v %= self.p;
        self
    }

    #[allow(dead_code)]
    pub fn inv(&mut self) -> &Self {
        let p = self.p;
        self.pow(p - 2);
        self
    }

    #[allow(dead_code)]
    pub fn pow(&mut self, mut n: usize) -> &Self {
        let mut temp = self.v;
        self.v = 1;
        while n > 0 {
            if n & 1 != 0 {
                self.v *= temp;
                self.v %= self.p;
            }
            n >>= 1;
            temp *= temp;
            temp %= self.p;
        }
        self
    }

    #[allow(dead_code)]
    pub fn get_value(&self) -> usize {
        self.v
    }
}

pub struct DPFactorial {
    p: usize,
    normal: Vec<Modint>,
    inv: Vec<Modint>,
}
impl DPFactorial {
    #[allow(dead_code)]
    pub fn new(p: usize) -> DPFactorial {
        let mut obj = DPFactorial {
            p: p,
            normal: Vec::new(),
            inv: Vec::new(),
        };
        obj.normal.push(Modint::from(p, 1));
        obj.inv.push(Modint::from(p, 1));
        obj
    }

    #[allow(dead_code)]
    pub fn get_factorial(&mut self, n: usize) -> Modint {
        if n < self.normal.len() {
            return self.normal[n].clone();
        }
        for z in self.normal.len()..n + 1 {
            let buf = Modint::from(self.p, z);
            let buf = &buf * &self.normal[z - 1];

            self.normal.push(buf);
        }
        return self.normal[n].clone();
    }

    #[allow(dead_code)]
    pub fn get_factorial_inv(&mut self, n: usize) -> Modint {
        if n < self.inv.len() {
            return self.inv[n].clone();
        }
        for z in self.inv.len()..n + 1 {
            let mut buf = Modint::from(self.p, z);
            buf.inv();
            let buf = &buf * &self.inv[z - 1];
            self.inv.push(buf);
        }
        self.inv[n].clone()
    }

    #[allow(dead_code)]
    pub fn get_combination(&mut self, n: usize, r: usize) -> Modint {
        if n < r {
            return Modint::from(self.p, 0);
        }
        &(&self.get_factorial(n) * &(self.get_factorial_inv(n - r))) * &(self.get_factorial_inv(r))
    }

    #[allow(dead_code)]
    pub fn get_permutation(&mut self, n: usize, r: usize) -> Modint {
        if n < r {
            return Modint::from(self.p, 0);
        }
        &self.get_factorial(n) * &(self.get_factorial_inv(n - r))
    }
}
}

#[macro_use]
mod prime_number {

use std::iter::Iterator;

pub struct PrimeFactorization {
    n: usize,
    cur: usize,
    limit: usize,
}

impl PrimeFactorization {
    pub fn calc(n: usize) -> PrimeFactorization {
        PrimeFactorization {
            n: n,
            cur: 1,
            limit: (n as f64).sqrt() as usize + 1,
        }
    }
}

impl Iterator for PrimeFactorization {
    type Item = usize;
    fn next(&mut self) -> Option<Self::Item> {
        loop {
            if self.cur == 0 || self.cur > self.n {
                return None;
            }

            self.cur += 1;

            if self.cur > self.limit {
                if self.n != 1 {
                    self.cur = 0;
                    return Some(self.n);
                }
                return None;
            }
            if self.n % self.cur == 0 {
                self.n /= self.cur;
                self.cur -= 1;
                return Some(self.cur + 1);
            }
        }
    }
}
}

use input::*;
use modint::*;
use prime_number::*;
#[allow(unused_imports)]
use std::collections::HashMap;

fn main() {
    let mut map = HashMap::new();
    let n: usize;
    input!(n);
    let mut ans = Modint::from(1_000_000_007, 1);
    for i in 0..n {
        for z in PrimeFactorization::calc(i + 1) {
            let po = map.entry(z).or_insert(0_usize);
            *po += 1;
        }
    }

    for (_, x) in map {
        ans.mul_uint(x+1);
    }
    p(ans);
}