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;
use std::io::Read;
use std::iter;

fn merge_sort(xs: &mut [usize], left: usize, right: usize) -> usize {
    if left + 1 < right {
        let mid = (left + right) / 2;
        let ncompleft = merge_sort(xs, left, mid);
        let ncompright = merge_sort(xs, mid, right);
        let ncompthis = merge(xs, left, mid, right);
        ncompleft + ncompright + ncompthis
    } else {
        0
    }
}

fn merge(xs: &mut [usize], left: usize, mid: usize, right: usize) -> usize {
    let l: Vec<usize> = xs[left..mid]
        .iter()
        .cloned()
        .chain(iter::once(std::usize::MAX))
        .collect();
    let r: Vec<usize> = xs[mid..right]
        .iter()
        .cloned()
        .chain(iter::once(std::usize::MAX))
        .collect();
    let mut i = 0;
    let mut j = 0;
    let mut ncomp = 0;

    for k in left..right {
        if l[i] <= r[j] {
            xs[k] = l[i].clone();
            i += 1;
        } else {
            xs[k] = r[j].clone();
            j += 1;
        }
        ncomp += 1;
    }

    ncomp
}

fn main() {
    let mut stdin = io::stdin();
    let mut buf = String::new();

    stdin.read_to_string(&mut buf);

    let mut iter = buf.split_whitespace();
    let n = iter.next().unwrap().parse().unwrap();
    let mut s: Vec<usize> = iter.map(|s| s.parse().unwrap()).collect();
    let cnt = merge_sort(&mut s, 0, n);
    println!(
        "{}",
        s.iter()
            .map(|s| s.to_string())
            .collect::<Vec<_>>()
            .join(" ")
    );
    println!("{}", cnt);
}