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.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;

public class Main {
	private static FastScanner sc = new FastScanner();
	static int cnt = 0;

	public static void main(String[] args) {
		int n = sc.nextInt();
		
		int[] A = new int[n];
		for(int i=0; i<n; i++) {
			A[i] = sc.nextInt();
		}
		
		mergeSort(A, 0, n);
		
		for(int i=0; i<n; i++) {
			System.out.print(A[i]);
			if(i != n-1) {
				System.out.print(" ");
			}
		}
		System.out.println();
		
		System.out.println(cnt);
	}
	
	static void merge(int A[], int left, int mid, int right) {
		int n1 = mid - left;
		int n2 = right - mid;
		int[] L = new int[n1 + 1];
		int[] R = new int[n2 + 1];
		for(int i=0; i<n1; i++) {
			L[i] = A[left + i];
		}
		for(int i=0; i<n2; i++) {
			R[i] = A[mid + i];
		}
		L[n1] = Integer.MAX_VALUE;
		R[n2] = Integer.MAX_VALUE;
		int i = 0;
		int j = 0;
		for(int k=left; k<right; k++) {
			if(L[i] <= R[j]) {
				A[k] = L[i];
				i++;
			} else {
				A[k] = R[j];
				j++;
			}
			cnt++;
		}
	}
	
	static void mergeSort(int[] A, int left, int right) {
		if(left + 1 < right) {
			int mid = (left + right) / 2;
			mergeSort(A, left, mid);
			mergeSort(A, mid, right);
			merge(A, left, mid, right);
		}
	}
	
	static class FastScanner {
	    private final InputStream in = System.in;
	    private final byte[] buffer = new byte[1024];
	    private int ptr = 0;
	    private int buflen = 0;
	    private boolean hasNextByte() {
	        if (ptr < buflen) {
	            return true;
	        }else{
	            ptr = 0;
	            try {
	                buflen = in.read(buffer);
	            } catch (IOException e) {
	                e.printStackTrace();
	            }
	            if (buflen <= 0) {
	                return false;
	            }
	        }
	        return true;
	    }
	    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	    private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
	    public boolean hasNext() { skipUnprintable(); return hasNextByte();}
	    public String next() {
	        if (!hasNext()) throw new NoSuchElementException();
	        StringBuilder sb = new StringBuilder();
	        int b = readByte();
	        while(isPrintableChar(b)) {
	            sb.appendCodePoint(b);
	            b = readByte();
	        }
	        return sb.toString();
	    }
	    public long nextLong() {
	        return Long.parseLong(next());
	    }
	    public int nextInt(){
	    	return Integer.parseInt(next());
	    }
	}
}