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.
# array de indices em ordem crescente
# quantos 2**b precisa para 2**v-1 (soma de sequencia)

import math

def main():
    n = int(input())
    a = input().split()
    a = [int(x) for x in a]
    
    p = 0
    carry = 0
    ok = 0
    while p<n:
        count = carry
        atual = a[p]
        while p<n and a[p] == atual:
            count += 1
            p += 1 
        if count%2 == 1:
            ok += 1
        carry = count//2 
        if p<n:       
            proximo = a[p]
        else:
            proximo = atual-1    
        while carry!= 0 and proximo!= atual+1:
            if carry%2 == 1:
                ok += 1
            carry = carry//2         
            atual += 1
    print(atual-ok+1)    

main()