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.util.Arrays;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class I {
	
	static void colocar(Set<Long> set,long n){
		if(set.contains(n)){
			set.remove(n);
			colocar(set,n+1);
		}else set.add(n);
	}
	
	public static void main(String[] args) {
		
	Scanner sc = new Scanner(System.in);
	long n = sc.nextLong();
	sc.nextLine();
	HashSet<Long> set= new HashSet<>();
	
	for (long i = 0; i < n; i++) {
		
		long novonum =sc.nextLong();
		colocar(set,novonum);
	}
	
	Long[] vetor=new Long[set.size()];
	vetor=set.toArray(vetor);
	Arrays.sort(vetor);
	
	System.out.print(vetor[vetor.length-1]-(set.size()-1));
	

	
	
	
		
		
	}

}
