Ivan has got an array of n non-negative integers a1, a2, ..., an. Ivan knows that the array is sorted in the non-decreasing order. 

Ivan wrote out integers 2a1, 2a2, ..., 2an on a piece of paper. Now he wonders, what minimum number of integers of form 2b (b ≥ 0) need to be added to the piece of paper so that the sum of all integers written on the paper equalled 2v - 1 for some integer v (v ≥ 0). 

Help Ivan, find the required quantity of numbers.

Input

The first line contains integer n (1 ≤ n ≤ 105). The second input line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 2·109). It is guaranteed that a1 ≤ a2 ≤ ... ≤ an.

Output

Print a single integer — the answer to the problem.

Examples

Input

4
0 1 1 1


Output

0


Input

1
3


Output

3

Note

In the first sample you do not need to add anything, the sum of numbers already equals 23 - 1 = 7.

In the second sample you need to add numbers 20, 21, 22.

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class TC
{
    static TreeMap<Long,Long> cnt;
    
    static void solve()
    {
        long curr = cnt.firstKey();
        long distinct=0;
        while( true )
        {
            long times=cnt.get( curr );
            if( times%2 == 1 )
                distinct++;
            long quot=times/2;
            long currPlus1=0;
            if( cnt.containsKey(curr+1))
                currPlus1=cnt.get( curr+1 );
            currPlus1+=quot;
            if( currPlus1 != 0 )
                cnt.put( curr+1, currPlus1 );
            cnt.put( curr, (long)0 );
            if( cnt.higherKey(curr) == null )
                break;
            else
                curr=cnt.higherKey(curr);
        }
        long MAX=curr;
        long res=MAX-distinct+1;
        System.out.println( res );
    }
    
    public static void main( String[] args ) throws IOException
    {
        BufferedReader br=new BufferedReader( new InputStreamReader( System.in ));
        int N=Integer.parseInt(br.readLine() );
        cnt=new TreeMap();
        String s=br.readLine();
        StringTokenizer tok=new StringTokenizer(s);
        for( int i=0; i<N; i++ )
        {
            long x=Integer.parseInt( tok.nextToken() );
            if( !cnt.containsKey(x))
                cnt.put( x, (long)1 );
            else
            {
               cnt.put( x, cnt.get(x)+1 );
            }
        }
        solve();
       
    }
}