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.
/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */

import java.io.*;
import java.util.*;

/**
 *
 * @author N-AssassiN
 */
public class Main {

    private static BufferedReader reader;
    private static BufferedWriter out;
    private static StringTokenizer tokenizer;
    //private final static String filename = "filename";

    /**
     * call this method to initialize reader for InputStream and OututStream
     */
    private static void init(InputStream input, OutputStream output) {
        reader = new BufferedReader(new InputStreamReader(input));
        out = new BufferedWriter(new OutputStreamWriter(output));
        //reader = new BufferedReader(new FileReader(filename + ".in"));
        //out = new BufferedWriter(new FileWriter(filename + ".out"));
        tokenizer = new StringTokenizer("");
    }

    /**
     * get next word
     */
    private static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

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

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

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

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException {
        init(System.in, System.out);
        int i;
        int n = nextInt();
        long[] a = new long[n];
        //long startTime = System.currentTimeMillis();
        for (i = 0; i < n; i++) {
            a[i] = nextLong();
        }
        long[] b = new long[n];
        int bSize = 0, aSize = n;
        boolean hasDuplicate = true, addToB = true;
        while (hasDuplicate) {
            hasDuplicate = false;
            if (addToB) {
                b = new long[aSize];
                bSize = 0;
                for (i = aSize - 1; i > 0; i--) {
                    if (a[i] == a[i - 1]) {
                        hasDuplicate = true;
                        b[bSize++] = (long) (1) + a[i];
                        i--;
                    } else {
                        b[bSize++] = a[i];
                    }
                }
                if (i >= 0) {
                    b[bSize++] = a[i];
                }
                addToB = false;
            } else {
                a = new long[bSize];
                aSize = 0;
                for (i = bSize - 1; i > 0; i--) {
                    if (b[i] == b[i - 1]) {
                        hasDuplicate = true;
                        a[aSize++] = (long) (1) + b[i];
                        i--;
                    } else {
                        a[aSize++] = b[i];
                    }
                }
                if (i >= 0) {
                    a[aSize++] = b[i];
                }
                addToB = true;
            }
        }
//        for (i = 0; i < aSize; i++) {
//            System.out.println("a " + a[i] + " b " + b[i]);
//        }
        if (addToB) {
            Arrays.sort(a);
            out.write((a[aSize - 1] + 1 - aSize) + "\n");
        } else {
            Arrays.sort(b);
            out.write((b[bSize - 1] + 1 - bSize) + "\n");
        }
        //long runTime = System.currentTimeMillis() - startTime;
        //out.write(runTime + "\n");
        out.flush();
    }
}