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.IOException;
import java.util.HashSet;
import java.util.StringTokenizer;

public class IvanAndPowersOfTwo {
	public static void main(String[] args) {
		MyScanner sc = new MyScanner();
		
		int N = sc.nextInt();
		
		long max = 0;
		BinCountSet bsc = new BinCountSet();
		for (int i = 0; i < N; i++) {
			long A = sc.nextLong();
			long v = bsc.insert(A);
			max = Math.max(max, v);
		}
		System.out.println(max - bsc.size() + 1);
	}
	
	public static class BinCountSet extends HashSet<Long> {
		private static final long serialVersionUID = 2492877876671495810L;
		
		public long insert(long k) {
			if (this.contains(k)) {
				this.remove(k);
				return this.insert(k + 1);
			} else {
				this.add(k);
				return k;
			}
		}
	}
	
	public static class MyScanner {
		BufferedReader br;
		StringTokenizer st;

		public MyScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		int nextInt() {
			return Integer.parseInt(next());
		}
		
		int[] nextIntArray(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

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

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

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		String nextLine() {
			String str = "";
			try { str = br.readLine(); }
			catch (IOException e) { e.printStackTrace(); }
			return str;
		}
	}
}