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.Scanner;


public class C {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		Twos twos = new Twos();
		twos.solve();
		twos.print();
	}

}


class Twos {

	Twos() {
		Scanner scr = new Scanner(System.in);
		n = scr.nextInt();
		a = new int[n];
		for (int i = 0; i < n; i++){
			a[i] = scr.nextInt();
		}
		scr.close();
	}
	
	void solve() {
		b2 = a[0];
		int i = 1;
		int k = 1;
		int ost = 0;
		while (i < n) {
			if (a[i] == a[i-1]){
				k++;
			}
			else {
				
				ost = ost + k;
				int st = 0;
				int t = ost;
				while (t > 0){
					st++;
					t /= 2;
				}
				if ((a[i] - a[i-1]) > st) {
					int da = a[i-1];
					while (ost > 0) {
						if (ost % 2 == 0){
							b2++;
						}
						ost = ost/2;
						da++;
					}
					da--;
					b2 += a[i] - da - 1;
				}
				else {
					st = 0;
					while ((a[i-1] + st) < a[i]){
						if (ost % 2 == 0){
							b2++;
						}
						ost = ost/2;
						st++;
					}
				}
				
				k = 1;
				
			}
			
			i++;
		}
		
		// 
		ost = ost + k;
		int st = 0;
		int t = ost;
		while (t > 0){
			st++;
			t /= 2;
		}
		
		st = st-1;
		while (ost > 0) {
		 	if (ost % 2 == 0){
				b2++;
			}
			ost = ost/2;
		}		
					
	}
	
	void print() {
		System.out.println(b2);
	}
	
	long b2;
	
	int n;
	int[] a;
}