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::str::FromStr;
use std::collections::{HashMap,HashSet,VecDeque,BinaryHeap};
use std::cmp::{max,min,Ordering};
use std::io::Read;

fn main() {

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

    let N = buf_it.next().unwrap().parse::<usize>().unwrap();
    let mut S = (0..N).map(|_| buf_it.next().unwrap().parse::<usize>().unwrap()).collect::<Vec<_>>();

    let cnt = mergeSort(&mut S,0,N);
    println!("{}",S.iter().map(|&s| format!("{}",s)).collect::<Vec<_>>().join(" "));
    println!("{}",cnt);

}

fn mergeSort(S:&mut Vec<usize>,left:usize,right:usize)->usize{
    let mut cnt = 0;
    if left+1 < right{
        let mid = (left + right)/2;
        cnt += mergeSort(S, left, mid);
        cnt += mergeSort(S, mid, right);
        cnt += merge(S,left,mid,right);
    }
    cnt
}

fn merge(S:&mut Vec<usize>,left:usize,mid:usize,right:usize)->usize{
    let mut cnt = 0;
    let mut L = (left..mid).map(|i| S[i]).collect::<Vec<_>>();
    let mut R = (mid..right).map(|i| S[i]).collect::<Vec<_>>();
    let INF = 1_000_100_000;
    L.push(INF);
    R.push(INF);
    let mut i = 0;
    let mut j = 0;
    for k in left..right{
        if L[i] <= R[j]{
            S[k] = L[i];
            i += 1;
        } else {
            S[k] = R[j];
            j += 1
        }
        cnt += 1;
    }
    cnt
}