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

public class _305C {

	static Scanner scanner = new Scanner(System.in);
	static int n, a, largest;
	static Set<Integer> m = new HashSet<Integer>();

	public static void main(String[] args) {
		n = scanner.nextInt();
		largest = -1;
		for (int i=0;i<n;++i) {
			a = scanner.nextInt();
			if (!m.contains(a)) {
				m.add(a);
				if (a >largest) {
					largest = a;
				}
			}
			else {
				do {
					m.remove(a);
					if (!m.contains(a+1)) {
						m.add(a+1);
						if (a + 1 > largest) {
							largest = a + 1;
						}
						break;
					}
					else {
						a = a+1;
					}
				} while(true);
			}
		}
		int ss = m.size();
		System.out.println(largest + 1 - ss);
	}

}
