Problem:
Score : 500 points

Problem Statement

Given are N positive integers A_1,...,A_N.

Consider positive integers B_1, ..., B_N that satisfy the following condition.

Condition: For any i, j such that 1 \leq i < j \leq N, A_i B_i = A_j B_j holds.

Find the minimum possible value of B_1 + ... + B_N for such B_1,...,B_N.

Since the answer can be enormous, print the sum modulo (10^9 +7).

Constraints

1 \leq N \leq 10^4

1 \leq A_i \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N

Output

Print the minimum possible value of B_1 + ... + B_N for B_1,...,B_N that satisfy the condition, modulo (10^9 +7).

Sample Input 1

3
2 3 4

Sample Output 1

13

Let B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.

Sample Input 2

5
12 12 12 12 12

Sample Output 2

5

We can let all B_i be 1.

Sample Input 3

3
1000000 999999 999998

Sample Output 3

996989508

Print the sum modulo (10^9+7).

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

//  ____            _                  _                       _       _
// |  _ \ _   _ ___| |_    ___ _ __   | |_ ___ _ __ ___  _ __ | | __ _| |_ ___
// | |_) | | | / __| __|  / __| '_ \  | __/ _ \ '_ ` _ \| '_ \| |/ _` | __/ _ \
// |  _ <| |_| \__ \ |_  | (__| |_) | | ||  __/ | | | | | |_) | | (_| | ||  __/
// |_| \_\\__,_|___/\__|  \___| .__/___\__\___|_| |_| |_| .__/|_|\__,_|\__\___|
//                            |_| |_____|               |_|

//https://github.com/manta1130/Competitive_Programming_Template_Rust

#[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 input_vector_row<T>(n: usize) -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::with_capacity(n);
        for _ in 0..n {
            let buf = match input_line_str().parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    pub trait ToCharVec {
        fn to_charvec(&self) -> Vec<char>;
    }

    impl ToCharVec for String {
        fn to_charvec(&self) -> Vec<char> {
            self.to_string().chars().collect::<Vec<_>>()
        }
    }
}

mod prime_number {

use std::iter::Iterator;

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

///素因数分解
impl PrimeFactorization {
    ///素因数を計算するイテレータを返す。
    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 prime_number::*;
use std::collections::BTreeMap;

fn main() {
    let n: usize;
    input!(n);
    let a = input_vector::<usize>();
    let mut v = vec![BTreeMap::new(); n];
    for i in 0..a.len() {
        for z in PrimeFactorization::calc(a[i]) {
            *v[i].entry(z).or_insert(0) += 1;
        }
    }

    let mut d = BTreeMap::new();

    for i in 0..v.len() {
        for (j, x) in v[i].iter() {
            if d.contains_key(j) {
                if d[&j] < x {
                    d.insert(j, x);
                }
            } else {
                d.insert(j, x);
            }
        }
    }

    let mut ans = 0;
    for i in 0..v.len() {
        let mut buf = 1;
        for (j, x) in d.iter() {
            let mut k = 0;
            if v[i].contains_key(&j) {
                k = v[i][*j];
            }
            buf *= j.pow((*x - k) as u32);
            buf %= 1_000_000_007;
        }
        ans += buf;
        ans %= 1_000_000_007;
    }
    println!("{}", ans);
}