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)

// ALDS1_5_B: Merge Sort

fn scan<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().parse().ok().unwrap()
}

fn scan_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s: String = scan();
    s.split_whitespace().map(|a| T::from_str(a).ok().unwrap()).collect()
}

fn merge(a: &mut Vec<i64>, left: usize, mid: usize, right: usize) -> usize {
    let mut l: Vec<i64> = Vec::new();
    let mut r: Vec<i64> = Vec::new();
    for i in left..mid {
        l.push(a[i]);
    }
    for i in mid..right {
        r.push(a[i]);
    }
    l.push(std::i64::MAX);
    r.push(std::i64::MAX);
    let mut i: usize = 0;
    let mut j: usize = 0;
    for k in left..right {
        if l[i] <= r[j] {
            a[k] = l[i];
            i += 1;
        } else {
            a[k] = r[j];
            j += 1;
        }
    }
    right - left
}

fn merge_sort(a: &mut Vec<i64>, left: usize, right: usize) -> usize {
    let mut cnt: usize = 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 n: usize = scan();
    let mut a: Vec<i64> = scan_vec();
    let cnt = merge_sort(&mut a, 0, n);
    let a = a.iter().map(|a| a.to_string()).collect::<Vec<String>>().join(" ");
    println!("{}", a);
    println!("{}", cnt);
}