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.
// package Practice.CF305;

import java.util.*;

public class CF305C {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        int[] arr = new int[n];
        HashSet<Integer> set = new HashSet<>();
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextInt();
            set.add(arr[i]);
        }
        HashMap<Integer, Integer> map = new HashMap<>();
        for (int i = 0; i < n; i++) {
            map.put(arr[i], map.getOrDefault(arr[i], 0) + 1);
        }

        Queue<Integer> queue = new LinkedList<Integer>();
        ArrayList<Integer> list = new ArrayList<>(set);
        int i = 0;
        int count = 0;
        int max = Integer.MIN_VALUE;
        while (i < list.size()) {
            int num;
            if (!queue.isEmpty() && list.get(i) > queue.peek()) {
                num = queue.poll();
            } else {
                num = list.get(i);
                i++;
            }
            max = Math.max(num, max);
            int m = map.get(num);
//            if(m >= 2){
            if (m % 2 != 0) {
                count++;
                m--;
            }
            if (m != 0) {
                if (map.containsKey(num + 1)) {
                    map.put(num + 1, map.get(num + 1) + m / 2);
                } else {
                    queue.add(num + 1);
                    map.put(num + 1, m / 2);
                }
            }
        }

        while(!queue.isEmpty()){
            int num = queue.poll();
            int m = map.get(num);
            max = Math.max(max, num);
//            if(m >= 2){
            if (m % 2 != 0) {
                count++;
                m--;
            }
            if (m != 0) {

                if (map.containsKey(num + 1)) {
                    map.put(num + 1, map.get(num + 1) + m / 2);
                } else {
                    queue.add(num + 1);
                    map.put(num + 1, m / 2);
                }
            }
        }
        System.out.println(max - count + 1);
    }
}
