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
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n)   FOR(i,0,n)
#define pb emplace_back
typedef long long ll;
typedef pair<int,int> pint;

int a[500001];
int INF=1000100010;
int cnt;
void merge(int l,int mid,int r){
    int cl=mid-l,cr=r-mid;
    vector<int> vl,vr;
    rep(i,cl) vl.pb(a[l+i]);
    rep(i,cr) vr.pb(a[mid+i]);
    vl.pb(INF),vr.pb(INF);
    cl=0,cr=0;
    FOR(i,l,r){
        if(vl[cl]<=vr[cr]) a[i]=vl[cl++];
        else a[i]=vr[cr++];
        ++cnt;
    }
}
void mergesort(int l,int r){
    if(r-l>1){
        int mid=(r+l)/2;
        mergesort(l,mid);
        mergesort(mid,r);
        merge(l,mid,r);
    }
}
int main(){
    int n;
    cin>>n;
    rep(i,n) cin>>a[i];
    mergesort(0,n);
    rep(i,n) cout<<a[i]<<(i==n-1?"":" ");
    cout<<endl;
    cout<<cnt<<endl;
    return 0;
}
