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.*;

public class C {

	private final static boolean autoflush = false;

	public C () {
		sc.nextInt();
		Long [] A = sc.nextLongs();

		TreeSet<Long> S = new TreeSet<Long>();
		for (long a : A)
			add(S, a);

		long M = S.last();
		long Q = S.size() - 1;
		long res = M - Q;
		exit(res);
	}

	void add(Set<Long> S, long x) {
		if (S.contains(x)) {
			S.remove(x);
			add(S, x+1);
		} else
			S.add(x);
	}

	////////////////////////////////////////////////////////////////////////////////////
	private final static MyScanner sc = new MyScanner();
	private static class MyScanner {
		public String next() { newLine(); return line[index++]; }
		public int nextInt() { return Integer.parseInt(next()); }
		public String nextLine() { line = null; return readLine(); }
		public String [] nextStrings() { return nextLine().split(" "); }
		public Long [] nextLongs() {
			String [] L = nextStrings();
			Long [] res = new Long [L.length];
			for (int i = 0; i < L.length; ++i)
				res[i] = Long.parseLong(L[i]);
			return res;
		}
		//////////////////////////////////////////////
		private boolean eol() { return index == line.length; }
		private String readLine() {
			try {
				return r.readLine();
			} catch (Exception e) {
				throw new Error (e);
			}
		}
		private final java.io.BufferedReader r;
		private MyScanner () { this(new java.io.BufferedReader(new java.io.InputStreamReader(System.in))); }
		private MyScanner (java.io.BufferedReader r) {
			try {
				this.r = r;
				while (!r.ready())
					Thread.sleep(1);
				start();
			} catch (Exception e) {
				throw new Error(e);
			}
		}
		private String [] line;
		private int index;
		private void newLine() {
			if (line == null || eol()) {
				line = readLine().split(" ");
				index = 0;
			}
		}
	}
	private static void print (Object o, Object... a) { printDelim(" ", o, a); }
	private static void printDelim (String delim, Object o, Object... a) { pw.println(build(delim, o, a)); }
	private static void exit (Object o, Object... a) { print(o, a); exit(); }
	private static void exit() {
		pw.close();
		System.out.flush();
		System.err.println("------------------");
		System.err.println("Time: " + ((millis() - t) / 1000.0));
		System.exit(0);
	}
	////////////////////////////////////////////////////////////////////////////////////
	private static String build (String delim, Object o, Object... a) {
		StringBuilder b = new StringBuilder();
		append(b, o, delim);
		for (Object p : a)
			append(b, p, delim);
		return b.substring(delim.length());
	}
	private static void append(StringBuilder b, Object o, String delim) {
		if (o.getClass().isArray()) {
			int L = java.lang.reflect.Array.getLength(o);
			for (int i = 0; i < L; ++i)
				append(b, java.lang.reflect.Array.get(o, i), delim);
		} else if (o instanceof Iterable<?>)
			for (Object p : (Iterable<?>)o)
				append(b, p, delim);
		else
			b.append(delim).append(o);
	}
	////////////////////////////////////////////////////////////////////////////////////
	private static void start() { t = millis(); }
	private static java.io.PrintWriter pw = new java.io.PrintWriter(System.out, autoflush);
	private static long t;
	private static long millis() { return System.currentTimeMillis(); }
	public static void main (String[] args) { new C(); exit(); }
}
