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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class IvanAndPowersOfTwo {
    public static void main(String[] args) throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(f.readLine());
        Pair[] a = new Pair[n];
        int index = 0;
        StringTokenizer st = new StringTokenizer(f.readLine());
        for (int i = 0; i < n; i++) {
            int x = Integer.parseInt(st.nextToken());
            if (index == 0 || a[index-1].x != x)
                a[index++] = new Pair(x,1);
            else
                a[index-1].y++;
        }
        int x = a[0].x;
        int y = a[0].y;
        int i2 = 1;
        int count = 0;
        while (y > 0 || i2 < index) {
            if (y % 2 == 1) 
                count++;
            x++;
            y /= 2;
            if (i2 < index && a[i2].x == x) 
                y += a[i2++].y;
            if (y == 0 && i2 < index) {
                x = a[i2].x;
                y = a[i2++].y;
            }
        }
        System.out.println(x-count);
    }
    
    public static class Pair {
        int x;
        int y;
        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }
}
