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 {

    static FastScanner sc = new FastScanner();
    static int n;
    static int[] A;
    static int c = 0;

    public static void main(String[] args) {
        n = Integer.parseInt(sc.next());
        A = new int[n];
        for (int i = 0; i < n; i++) {
            A[i] = Integer.parseInt(sc.next());
        }

        mergeSort(0, n);

        for (int i = 0; i < n; i++) {
            if (i != n - 1) {
                System.out.print(String.format("%d ", A[i]));
            } else {
                System.out.print(String.format("%d\n", A[i]));
            }
        }
        System.out.println(c);
    }

    static void merge(int l, int m, int r) {
        int n1 = m - l, n2 = r - m;
        int[] L = new int[n1 + 1];
        int[] R = new int[n2 + 1];

        for (int i = 0; i < n1; i++) {
            L[i] = A[l + i];
        }

        for (int i = 0; i < n2; i++) {
            R[i] = A[m + i];
        }

        L[n1] = 1 << 31 - 1;
        R[n2] = 1 << 31 - 1;

        int i = 0, j = 0;
        for (int k = l; k < r; k++) {
            c++;

            if (L[i] <= R[j]) {
                A[k] = L[i];
                i++;
            } else {
                A[k] = R[j];
                j++;
            }
        }
    }

    static void mergeSort(int l, int r) {
        if (l + 1 < r) {
            int m = (r + l) / 2;
            mergeSort(l, m);
            mergeSort(m, r);
            merge(l, m, r);
        }
    }
}

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() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
}