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.
// practice with kaiboy
import java.io.*;
import java.util.*;

public class CF305C extends PrintWriter {
	CF305C() { super(System.out, true); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		CF305C o = new CF305C(); o.main(); o.flush();
	}

	void main() {
		int n = sc.nextInt();
		int[] aa = new int[n];
		for (int i = 0; i < n; i++)
			aa[i] = sc.nextInt();
		int cnt = 0;
		for (int i = 0, j = 0; i < n; ) {
			while (j < n && aa[j] == aa[i])
				j++;
			int k = j - i;
			cnt += k & 1;
			i = j - k / 2;
			for (int h = i; h < j; h++)
				aa[h]++;
		}
		println(aa[n - 1] + 1 - cnt);
	}
}
