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.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class PowersOfTwo {
    public static void main(String[] args) {
        TreeSet<Integer> s = new TreeSet<>();

        int maxIter = 0;

        int n = nextInt();
        for (int i = 0; i < n; i++) {
            int c = nextInt();
            if (s.contains(c)) {
                int t = c;
                int curIter = 0;
                while (s.contains(t)) {
                    t++;
                    curIter++;
                }

                maxIter = Math.max(maxIter, curIter);

                s.add(t);
                s.tailSet(c, true).headSet(t, false).clear();
            } else s.add(c);
        }

        writer.println(s.last() - s.size() + 1);
        System.err.println("maxIter : " + maxIter);
        writer.close();
    }

    static PrintWriter writer = new PrintWriter(System.out);

    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer tokenizer = new StringTokenizer("");

    static String next() {
        while (!tokenizer.hasMoreTokens())
            try {
                tokenizer = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                return null;
            }
        return tokenizer.nextToken();
    }

    static int nextInt() {
        return Integer.parseInt(next());
    }

    static long nextLong() {
        return Long.parseLong(next());
    }

    static double nextDouble() {
        return Double.parseDouble(next());
    }
}