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)

fn main() {
    // 数列の長さ
    let n: usize = read()[0];

    // ランダムな数列
    let mut s: Vec<i32> = read();

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

// 一行読み込みを行う
fn read<T: std::str::FromStr>() -> Vec<T> {
    let mut buf = String::new();
    let stdin = std::io::stdin();
    stdin.read_line(&mut buf).unwrap();
    buf.split_whitespace().flat_map(str::parse).collect()
}

fn merge_sort(a: &mut Vec<i32>, left: usize, right: usize) -> usize {
    let mut count = 0;
    if left + 1 < right {
        let mid: usize = (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<i32>, left: usize, mid: usize, right: usize) -> usize {
    // リストの左側を作成
    let mut left_array = a[left..mid].to_vec();

    // リストの右側を作成
    let mut right_array = a[mid..right].to_vec();

    // 終端追加
    left_array.push(std::i32::MAX);
    right_array.push(std::i32::MAX);

    let mut i = 0;
    let mut j = 0;
    for k in left..right {
        if left_array[i] <= right_array[j] {
            a[k] = left_array[i];
            i += 1;
        } else {
            a[k] = right_array[j];
            j += 1;
        }
    }

    // iとjを合算が比較回数となる
    i + j
}