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)

#[allow(unused_imports)]
use std::cmp::{max, min};
use std::io::{stdin, stdout, BufWriter, Write};

#[derive(Default)]
struct Scanner {
    buffer: Vec<String>,
}

impl Scanner {
    fn next<T: std::str::FromStr>(&mut self) -> T {
        loop {
            if let Some(token) = self.buffer.pop() {
                return token.parse().ok().expect("Failed parse");
            }
            let mut input = String::new();
            stdin().read_line(&mut input).expect("Failed read");
            self.buffer = input.split_whitespace().rev().map(String::from).collect();
        }
    }
}

fn merge(a: &mut [i32], left: usize, mid: usize, right: usize) -> i32{
    let n1 = mid - left;
    let n2 = right - mid;
    let mut l = vec![0; n1];
    let mut r = vec![0; n2];
    l.copy_from_slice(&a[left..mid]);
    r.copy_from_slice(&a[mid..right]);
    l.push(std::i32::MAX);
    r.push(std::i32::MAX);
    let mut i = 0;
    let mut j = 0;
    let mut cnt = 0;
    for k in left..right {
        cnt+=1;
        if l[i] <= r[j] {
            a[k] = l[i];
            i += 1;
        } else {
            a[k] = r[j];
            j += 1;
        }
    }
    cnt
}

fn merge_sort(a: &mut[i32], left: usize, right: usize) -> i32{
    let mut cnt = 0;
    if left + 1 < right {
        let mid = (left + right) / 2;
        cnt += merge_sort(a, left, mid);
        cnt += merge_sort(a, mid, right);
        cnt += merge(a, left, mid, right);
    }
    cnt
}

fn main() {
    let mut sc = Scanner::default();
    let out = &mut BufWriter::new(stdout());
    let n = sc.next();
    let mut a = Vec::new();
    for _ in 0..n {
        let x: i32 = sc.next();
        a.push(x);
    }
    let cnt = merge_sort(&mut a[..], 0, n);
    let a = a.iter().map(ToString::to_string).collect::<Vec<String>>().join(" ");
    writeln!(out, "{}", a).ok();
    writeln!(out, "{}", cnt).ok();
}