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.*;
import java.util.*;
public class Main {
    public static void main(String[] args) throws IOException {
        init(System.in, System.out);
        int i;
        int n = nextInt();
        long[] a = new long[n];
        for (i = 0; i < n; i++) {
            a[i] = nextLong();
        }
        long[] b = new long[n];
        int aLength = n, bLength = 0;
        boolean hasDuplicate = true, addToB = true;
        while (hasDuplicate) {
            hasDuplicate = false;
            if (addToB) {
                b = new long[aLength];
                bLength = 0;
                for (i = 0; i < aLength-1; i++) {
                    if (a[i] == a[i + 1]) {
                        hasDuplicate = true;
                        b[bLength++] = a[i]+1;
                        i++;
                    } else {
                        b[bLength++] = a[i];
                    }
                }
                if (i == aLength-1) {
                    b[bLength++] = a[i];
                }
                addToB = false;
            } else {
                a = new long[bLength];
                aLength = 0;
                for (i = 0; i < bLength-1; i++) {
                    if (b[i] == b[i + 1]) {
                        hasDuplicate = true;
                        a[aLength++] = b[i]+1;
                        i++;
                    } else {
                        a[aLength++] = b[i];
                    }
                }
                if (i ==bLength-1) {
                    a[aLength++] = b[i];
                }
                addToB = true;
            }
        }
        aLength--;
        bLength--;
        if (addToB) {
            Arrays.sort(a);
            out.write((a[aLength]- aLength) + "\n");
        } else {
            Arrays.sort(b);
            out.write((b[bLength] - bLength) + "\n");
        }
        out.flush();
    }
    private static BufferedReader reader;
    private static BufferedWriter out;
    private static StringTokenizer tokenizer;

    private static void init(InputStream input, OutputStream output) {
        reader = new BufferedReader(new InputStreamReader(input));
        out = new BufferedWriter(new OutputStreamWriter(output));
        tokenizer = new StringTokenizer("");
    }

    private static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            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());
    }
}