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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;
import java.io.BufferedWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.IOException;
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Alex
 */
public class Main{
	public static void main(String[] args){
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}
	static class TaskC{
		public void solve(int testNumber, InputReader in, OutputWriter out){
			int MAXVAL = 100009;
			int n = in.ri();
			int[] a = IOUtils.readIntArray(in, n);
			int[] count = new int[MAXVAL];
			int[] res = new int[MAXVAL];
			for(int i = 0; i < n; i++) {
				int initval = a[i], val = a[i], tohere = 0;
				while(val > 0){
					int valcopy = val, tovalcopy = tohere;
					while(valcopy < MAXVAL){
						if(count[valcopy] == i){
							res[valcopy] += tovalcopy;
							count[valcopy]++;
						}
						valcopy *= 2;
						tovalcopy++;
					}
					val /= 2;
					tohere++;
				}
			}
			int ans = Integer.MAX_VALUE;
			for(int i = 0; i < MAXVAL; i++) {
				if(count[i] == n) ans = Math.min(ans, res[i]);
			}
			out.printLine(ans);
		}
	}
	static class OutputWriter{
		private final PrintWriter writer;
		public OutputWriter(OutputStream outputStream){
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}
		public OutputWriter(Writer writer){
			this.writer = new PrintWriter(writer);
		}
		public void close(){
			writer.close();
		}
		public void printLine(int i){
			writer.println(i);
		}
	}
	static class InputReader{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private InputReader.SpaceCharFilter filter;
		public InputReader(InputStream stream){
			this.stream = stream;
		}
		public int read(){
			if(numChars == -1)
				throw new InputMismatchException();
			if(curChar >= numChars){
				curChar = 0;
				try{
					numChars = stream.read(buf);
				} catch(IOException e){
					throw new InputMismatchException();
				}
				if(numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
		public int ri(){
			return readInt();
		}
		public int readInt(){
			int c = read();
			while(isSpaceChar(c))
				c = read();
			int sgn = 1;
			if(c == '-'){
				sgn = -1;
				c = read();
			}
			int res = 0;
			do{
				if(c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while(!isSpaceChar(c));
			return res * sgn;
		}
		public boolean isSpaceChar(int c){
			if(filter != null)
				return filter.isSpaceChar(c);
			return isWhitespace(c);
		}
		public static boolean isWhitespace(int c){
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
		public interface SpaceCharFilter{
			public boolean isSpaceChar(int ch);
		}
	}
	static class IOUtils{
		public static int[] readIntArray(InputReader in, int size){
			int[] array = new int[size];
			for(int i = 0; i < size; i++)
				array[i] = in.readInt();
			return array;
		}
	}
}

