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)

// This code is generated by cargo-atcoder

// Original source code:
/*
#[macro_use]
extern crate competitive;

use competitive::modular::Mod;

fn fact(mut n: i64) -> Vec<(i64, usize)> {
    let mut ret = vec![];
    for i in 2.. {
        if i * i > n {
            break;
        }

        let mut cnt = 0;

        while n % i == 0 {
            cnt += 1;
            n /= i;
        }

        ret.push((i, cnt));
    }

    if n != 1 {
        ret.push((n, 1));
    }

    ret
}

use std::cmp::max;
use std::collections::BTreeMap;

fn main() {
    input! {
        n: usize,
        a: [i64; n],
    }

    let mut ps = BTreeMap::new();

    for &a in a.iter() {
        for (p, n) in fact(a) {
            let r = ps.entry(p).or_default();
            *r = max(*r, n);
        }
    }

    let mut lcm = Mod::new(1);
    for (p, n) in ps {
        lcm *= Mod::new(p).pow(n as i64);
    }

    let mut ans = Mod::new(0);
    for a in a {
        let b = lcm / Mod::new(a);
        ans += b;
    }

    println!("{}", ans);
}

*/

fn main() {
    let exe = "./binXXXXXX";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().enumerate() {
        if c == b'=' { break; }
        let c = tbl[c as usize];
        if c == 64 { continue; }
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";