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.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Map.Entry;

public class C {
    public static int solve(int[] A) {
        HashMap<Integer, Integer> H = new HashMap<Integer, Integer>();
        for (int i = 0; i < A.length;) {
            int j = i;
            while (j < A.length && A[j] == A[i])
                j++;
            int cnt = j - i;
            if (H.containsKey(A[i])) {
                cnt += H.get(A[i]);
                H.remove(A[i]);
            }
            for (int k = 0; k < 32; k++)
                if ((cnt & (1 << k)) != 0) {
                    if (H.containsKey(A[i] + k))
                        H.put(A[i] + k, H.get(A[i] + k) + 1);
                    else
                        H.put(A[i] + k, 1);
                }
            i = j;
        }
        int tot = 0;
        for (Entry<Integer, Integer> e : H.entrySet())
            tot += e.getValue();
        if (tot == H.size()) {
            int[] K = new int[tot + 1];
            K[0] = -1;
            int index = 1;
            for (Entry<Integer, Integer> e : H.entrySet())
                K[index++] = e.getKey();
            Arrays.sort(K);
            int ans = 0;
            for (int i = 1; i < K.length; i++)
                ans += K[i] - K[i - 1] - 1;
            return ans;
        } else {
            int[] K = new int[tot];
            int index = 0;
            for (Entry<Integer, Integer> e : H.entrySet()) {
                int v = e.getValue();
                while (v-- > 0)
                    K[index++] = e.getKey();
            }
            return solve(K);
        }
    }

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        int n = in.readInt();
        int[] A = new int[n];
        for (int i = 0; i < n; i++)
            A[i] = in.readInt();
        System.out.println(solve(A));
    }
}

class InputReader {

    private InputStream stream;
    private byte[] buf = new byte[1000];
    private int curChar, numChars;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    private int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int readInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public long readLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public String readString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuffer res = new StringBuffer();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    private boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private String readLine0() {
        StringBuffer buf = new StringBuffer();
        int c = read();
        while (c != '\n' && c != -1) {
            buf.appendCodePoint(c);
            c = read();
        }
        return buf.toString();
    }

    public String readLine() {
        String s = readLine0();
        while (s.trim().length() == 0)
            s = readLine0();
        return s;
    }

    public String readLine(boolean ignoreEmptyLines) {
        if (ignoreEmptyLines)
            return readLine();
        else
            return readLine0();
    }

    public char readCharacter() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        return (char) c;
    }

    public double readDouble() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E')
                return res * Math.pow(10, readInt());
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, readInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }
}