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 ProblemC {

    public void solve() {
        Scanner scan = new Scanner(System.in);

        int n = scan.nextInt();

        int prev = 0;
        int pc = 0;
        int count = 0;
        for (int i = 0; i < n; i++) {
            int a = scan.nextInt();
            if (prev != a) {
                for (int j = prev; j < a; j++) {
                    if (pc % 2 == 0) {
                        count++;
                    }
                    pc = pc / 2;
                    if (pc == 0) {
                        count += a - j - 1;
                        break;
                    }
                }
            }
            pc++;
            prev = a;
        }

        while (pc > 0) {
            if (pc % 2 == 0) {
                count++;
            }
            pc = pc / 2;
        }

        System.out.println(count);
    }

    public static void main(String[] args) {
        ProblemC c = new ProblemC();
        c.solve();
    }
}