Problem:
Merge Sort

Write a program of a Merge Sort algorithm implemented by the following pseudocode. You should also report the number of comparisons in the Merge function.

Merge(A, left, mid, right)
n1 = mid - left;
n2 = right - mid;
create array L[0...n1], R[0...n2]
for i = 0 to n1-1
do L[i] = A[left + i]
for i = 0 to n2-1
do R[i] = A[mid + i]
L[n1] = SENTINEL
R[n2] = SENTINEL
i = 0;
j = 0;
for k = left to right-1
if L[i] <= R[j]
then A[k] = L[i]
i = i + 1
else A[k] = R[j]
j = j + 1

Merge-Sort(A, left, right){
if left+1 < right
then mid = (left + right)/2;
call Merge-Sort(A, left, mid)
call Merge-Sort(A, mid, right)
call Merge(A, left, mid, right)

Input

In the first line n is given. In the second line, n integers are given.

Output

In the first line, print the sequence S. Two consequtive elements should be separated by a space character.

In the second line, print the number of comparisons.

Constraints

n ≤ 500000

0 ≤ an element in S ≤ 109

Sample Input 1

10
8 5 9 2 6 3 7 1 10 4

Sample Output 1

1 2 3 4 5 6 7 8 9 10
34

Notes

Solution in Rust (judge verdict: Accepted)

use std::io::{stdin, Read};

fn main() {
    let mut buf = String::new();
    stdin().read_to_string(&mut buf).unwrap();
    let mut iterator = buf.split_whitespace();

    let n: isize = iterator.next().unwrap().parse().unwrap();

    let mut s = iterator
        .map(|s| s.parse::<isize>().unwrap())
        .collect::<Vec<_>>();

    let count = merge_sort(&mut s, 0, n);
    println!(
        "{}",
        s.into_iter().map(|x| x.to_string()).collect::<Vec<String>>().join(" ")
    );
    println!("{}", count);
}

fn merge_sort(a: &mut Vec<isize>, left: isize, right: isize) -> usize {
    let mut count = 0;
    if left + 1 < right {
        let mid = (left + right) / 2;
        count += merge_sort(a, left, mid);
        count += merge_sort(a, mid, right);
        count += merge(a, left, mid, right);
    }
    count
}

fn merge(a: &mut Vec<isize>, left: isize, mid: isize, right: isize) -> usize {
    let n1 = mid - left;
    let n2 = right - mid;

    let mut l: Vec<isize> = Vec::new();
    for i in 0..n1 {
        l.push(a[(left + i) as usize]);
    }
    l.push(std::isize::MAX);

    let mut r: Vec<isize> = Vec::new();
    for i in 0..n2 {
        r.push(a[(mid + i) as usize]);
    }
    r.push(std::isize::MAX);

    let mut i = 0;
    let mut j = 0;
    for k in left..right {
        if l[i] <= r[j] {
            a[k as usize] = l[i];
            i += 1;
        } else {
            a[k as usize] = r[j];
            j += 1;
        }
    }
    i + j
}