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)


Notes

Constraints

* n ≤ 500000
* 0 ≤ an element in S ≤ 109

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.

Example

Input

10
8 5 9 2 6 3 7 1 10 4


Output

1 2 3 4 5 6 7 8 9 10
34
import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {

	public static void main(String[] args) throws Exception {
		// TODO ?????????????????????????????????????????????
		BufferedReader br =
				new BufferedReader( new InputStreamReader(System.in) );
		int n = Integer.parseInt(br.readLine());

		String[] data = br.readLine().split(" ");
		int[] S = new int[n];
		for (int i=0; i < n; i++) {
			S[i] = Integer.parseInt(data[i]);
		}

		int count = mergeSort(S, 0, n);
		System.out.print(S[0]);
		for (int i=1; i < n; i++) {
			System.out.print(" " + S[i]);
		}
		System.out.println();
		System.out.println(count);
	}

	/**
	 * A???????´?????????????l <= index < r ??¨????????¨???????????????
	 * l??\???m???????????¨???L??¨???m??\???r???????????¨???R????????§??????????????´?????????????????¨??????
	 * ????????????????????????????????????????????????????????´??????????????????????????????
	 * L???????°????????´???¨???R???????°????????´??????????????°?????????????
	 * L??¨R????????§????°????????´???¨?????????
	 */
	static int merge(int[] A, int l, int m, int r) { // l:left, m:mid, r:right
		int n1 = m - l;
		int n2 = r - m;

		int max = A[l]; //bannpei
		// L = {A[l], A[l+1], A[l+2], ... , A[m-2], A[m-1], bannpei}
		int[] L = new int[n1+1];
		for (int i=0; i < n1; i++) {
			L[i] = A[l+i];
			if (max < L[i]) {
				max = L[i];
			}
		}

		// R = {A[m], A[m+1], ... , A[r-1], bannpei}
		int[] R = new int[n2+1];
		for (int i=0; i < n2; i++) {
			R[i] = A[m+i];
			if (max < R[i]) {
				max = R[i];
			}
		}

		// bannpei?¨????
		max += 1;
		L[n1] = max;
		R[n2] = max;

		int i = 0;
		int j = 0;
		int count = 0;
		for (int k = l; k < r; k++) {
			count++;
			if ( L[i] <= R[j] ) {
				A[k] = L[i];
				i++;
			} else {
				A[k] = R[j];
				j++;
			}
		}
		return count;
	}

	/**
	 * A????????????l <= index < r??¨????????¨?????????????????´????????????
	 */
	static int mergeSort(int[] A, int l, int r) {
		int count = 0;
		if ( l+1 < r ) {
			int m = (l+r) / 2;
			count += mergeSort(A, l, m);
			count += mergeSort(A, m, r);
			count += merge(A, l, m, r);
		}
		return count;
	}
}