Amr loves Chemistry, and specially doing experiments. He is preparing for a new interesting experiment.

Amr has n different types of chemicals. Each chemical i has an initial volume of ai liters. For this experiment, Amr has to mix all the chemicals together, but all the chemicals volumes must be equal first. So his task is to make all the chemicals volumes equal.

To do this, Amr can do two different kind of operations. 

  * Choose some chemical i and double its current volume so the new volume will be 2ai
  * Choose some chemical i and divide its volume by two (integer division) so the new volume will be <image>



Suppose that each chemical is contained in a vessel of infinite volume. Now Amr wonders what is the minimum number of operations required to make all the chemicals volumes equal?

Input

The first line contains one number n (1 ≤ n ≤ 105), the number of chemicals.

The second line contains n space separated integers ai (1 ≤ ai ≤ 105), representing the initial volume of the i-th chemical in liters.

Output

Output one integer the minimum number of operations required to make all the chemicals volumes equal.

Examples

Input

3
4 8 2


Output

2

Input

3
3 5 6


Output

5

Note

In the first sample test, the optimal solution is to divide the second chemical volume by two, and multiply the third chemical volume by two to make all the volumes equal 4.

In the second sample test, the optimal solution is to divide the first chemical volume by two, and divide the second and the third chemical volumes by two twice to make all the volumes equal 1.
import java.io.InputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.ArrayDeque;
import java.util.Comparator;
import java.util.Deque;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;
import java.math.BigDecimal;
import java.math.BigInteger;
    
public class Main{
 
static PrintWriter out;
static InputReader ir;
static final int MAX_N=(int)1e5+1,INF=(int)1e9;
static int[] visited=new int[MAX_N],cnt=new int[MAX_N],step=new int[MAX_N];

static void solve(){
 int n=ir.nextInt();
 int[] a=ir.nextIntArray(n);
 for(int i=0;i<n;i++){
  Deque<Pair> que=new ArrayDeque<>();
  que.add(new Pair(a[i],0));
  while(!que.isEmpty()){
   Pair p=que.pollFirst();
   if(p.x>=MAX_N||visited[p.x]==i+1) continue;
   visited[p.x]=i+1;
   step[p.x]+=p.y;
   cnt[p.x]++;
   que.offerLast(new Pair(p.x*2,p.y+1));
   que.offerLast(new Pair(p.x/2,p.y+1));
  }
 }
 int mi=INF;
 for(int i=0;i<MAX_N;i++){
  if(cnt[i]==n) mi=Math.min(mi,step[i]);
 }
 out.println(mi);
}

static class Pair{
 int x;
 int y;
 public Pair(int x,int y){
  this.x=x; this.y=y;
 }
 public static Comparator<Pair> X_ORDER=new Comp1();
 public static Comparator<Pair> Y_ORDER=new Comp2();
 private static class Comp1 implements Comparator<Pair>{
  public int compare(Pair p1,Pair p2){
   return (p1.x>p2.x)?1:(p1.x<p2.x)?-1:0;
  }
 }
 private static class Comp2 implements Comparator<Pair>{
  public int compare(Pair p1,Pair p2){
   return (p1.y>p2.y)?1:(p1.y<p2.y)?-1:0;
  }
 }
}

public static void main(String[] args) throws Exception{
 ir=new InputReader(System.in);
 out=new PrintWriter(System.out);
 solve();
 out.flush();
}

static class InputReader {
 private InputStream in;
 private byte[] buffer=new byte[1024];
 private int curbuf;
 private int lenbuf;

 public InputReader(InputStream in) {this.in=in; this.curbuf=this.lenbuf=0;}
 
 public boolean hasNextByte() {
  if(curbuf>=lenbuf){
   curbuf= 0;
   try{
    lenbuf=in.read(buffer);
   }catch(IOException e) {
    throw new InputMismatchException();
   }
   if(lenbuf<=0) return false;
  }
  return true;
 }

 private int readByte(){if(hasNextByte()) return buffer[curbuf++]; else return -1;}
 
 private boolean isSpaceChar(int c){return !(c>=33&&c<=126);}
 
 private void skip(){while(hasNextByte()&&isSpaceChar(buffer[curbuf])) curbuf++;}
 
 public boolean hasNext(){skip(); return hasNextByte();}
 
 public String next(){
  if(!hasNext()) throw new NoSuchElementException();
  StringBuilder sb=new StringBuilder();
  int b=readByte();
  while(!isSpaceChar(b)){
   sb.appendCodePoint(b);
   b=readByte();
  }
  return sb.toString();
 }
 
 public int nextInt() {
  if(!hasNext()) throw new NoSuchElementException();
  int c=readByte();
  while (isSpaceChar(c)) c=readByte();
  boolean minus=false;
  if (c=='-') {
   minus=true;
   c=readByte();
  }
  int res=0;
  do{
   if(c<'0'||c>'9') throw new InputMismatchException();
   res=res*10+c-'0';
   c=readByte();
  }while(!isSpaceChar(c));
  return (minus)?-res:res;
 }
 
 public long nextLong() {
  if(!hasNext()) throw new NoSuchElementException();
  int c=readByte();
  while (isSpaceChar(c)) c=readByte();
  boolean minus=false;
  if (c=='-') {
   minus=true;
   c=readByte();
  }
  long res = 0;
  do{
   if(c<'0'||c>'9') throw new InputMismatchException();
   res=res*10+c-'0';
   c=readByte();
  }while(!isSpaceChar(c));
  return (minus)?-res:res;
 }

 public double nextDouble(){return Double.parseDouble(next());}

 public BigInteger nextBigInteger(){return new BigInteger(next());}

 public int[] nextIntArray(int n){
  int[] a=new int[n];
  for(int i=0;i<n;i++) a[i]=nextInt();
  return a;
 }

 public long[] nextLongArray(int n){
  long[] a=new long[n];
  for(int i=0;i<n;i++) a[i]=nextLong();
  return a;
 }

 public char[][] nextCharMap(int n,int m){
  char[][] map=new char[n][m];
  for(int i=0;i<n;i++) map[i]=next().toCharArray();
  return map;
 }
}
}