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;

fn main() {
    let _ = read_vec::<i32>();
    let mut a = read_vec::<i32>();
    let len = a.len();

    let count = merge_sort(&mut a, 0, len);
    print_vec(a);
    println!("{}", count);
}

pub fn merge(a: &mut [i32], left: usize, mid: usize, right: usize) -> usize {
    let mut count = 0;
    let mut l = a[left..mid].to_vec();
    let mut r = a[mid..right].to_vec();
    // 番兵の挿入
    l.push(std::i32::MAX);
    r.push(std::i32::MAX);
    let mut i = 0;
    let mut j = 0;
    for k in left..right {
        if l[i] <= r[j] {
            a[k] = l[i];
            i += 1;
        } else {
            a[k] = r[j];
            j += 1;
        }
        count += 1;
    }
    count
}

pub fn merge_sort(a: &mut [i32], left: usize, right: usize) -> 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
}

/// 標準入力から一行を読み取り、空白文字で分割し、各要素を指定の型に変換する関数
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut line = String::new();
    io::stdin().read_line(&mut line)
        .ok()
        .expect("Faild to read Vec");
    line.trim().split_whitespace()
        .map(|i| i.parse().ok().unwrap()).collect()
}

fn print_vec<T: std::fmt::Display>(v: Vec<T>) {
    for a in &v[0..v.len() - 1] {
        print!("{} ", a);
    }
    println!("{}", v[v.len() - 1]);
}