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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;


public class C {
    
    static StringTokenizer st;
    static BufferedReader in;
    static PrintWriter pw;
    
    public static void main(String[] args) throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n = nextInt();
        int[]a = new int[n+2];
        for (int i = 1; i <= n; i++) {
            a[i] = nextInt();
        }
        int begin = 1;
        int[]power = new int[(int) 2e5], cnt = new int[(int) 2e5];
        int t = 0;
        a[n+1] = -1;
        for (int i = 2; i <= n+1; i++) {
            if (a[i] != a[i-1]) {
                cnt[++t] = i-begin;
                power[t] = a[i-1];
                begin = i;
            }
        }
        int exist = 0;
        power[t+1] = Integer.MAX_VALUE;
        int max = 0;
        for (int i = 1; i <= t; i++) {
            int pow = power[i], cn = cnt[i];
            while (cn > 0 && pow != power[i+1]) {
                if (cn % 2==1)
                    exist++;
                cn /= 2;
                if (cn==0)
                    break;
                pow++;
            }
            if (pow==power[i+1])
                cnt[i+1] += cn;
            max = Math.max(max, pow);
        }
        System.out.println(max-exist+1);
        pw.close();
    }
    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());
    }
    
    private static String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }
}
