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 read_string() -> String {
    use std::io::Read;

    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    return buf;
}

static mut COMP_COUNT: u32 = 0;

fn main() {
    let input = read_string();
    let input = input.lines().collect::<Vec<_>>();
    let n: usize = input[0].parse().unwrap();
    let mut series = input[1].split_whitespace().map(|s| s.parse().unwrap()).collect::<Vec<u32>>();
    merge_sort(&mut series, 0, n);

    println!("{}", series.into_iter().map(|e| format!("{}", e)).collect::<Vec<String>>().join(" "));
    unsafe {
        println!("{}", COMP_COUNT);
    }
}

fn merge(series: &mut Vec<u32>, left: usize, mid: usize, right: usize) {
    let mut ls = series[left..mid].to_vec();
    ls.push(std::u32::MAX);
    let mut rs = series[mid..right].to_vec();
    rs.push(std::u32::MAX);

    let mut li = 0;
    let mut ri = 0;
    for i in left..right {
        unsafe {
            COMP_COUNT += 1;
        }
        if ls[li] >= rs[ri] {
            series[i] = rs[ri];
            ri += 1;
        } else {
            series[i] = ls[li];
            li += 1;
        }
    }
}

fn merge_sort(series: &mut Vec<u32>, left: usize, right: usize) {
    if left + 1 < right {
        let mid = (left + right) / 2;
        merge_sort(series, left, mid);
        merge_sort(series, mid, right);
        merge(series, left, mid, right);
    }
}