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 math
n = input()
a =  map(int, raw_input().split())+[2*(10**10)]
b = []
cnt = 1
while 1:
    for i in xrange(len(a)-1):
        if a[i] == a[i+1]:
            cnt += 1
            continue
        else:
            if cnt == 1:
                b.append(a[i])
                continue
            else:
                repo = []
                while cnt > 0:
                    tmp = int(math.log(cnt, 2))
                    repo.append(tmp+a[i])
                    cnt = cnt-2**tmp
                a = repo + a[i+1:]
                a.sort()
                cnt = 1
                break
    else:
        break
ans = 0
for i in xrange(len(b)-1, -1, -1):
    if i == 0:
        if b[i] != 0:
            ans += b[i]
    elif b[i]-b[i-1] > 1:
        ans += b[i]-b[i-1]-1
print ans