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.
n = int(raw_input())
line = raw_input().split()
a = [[int(line[0]), 1]]
na = 1
for i in range(1, n):
    x = int(line[i])
    if a[na - 1][0] == x:
        a[na - 1][1] += 1
    else:
        a.append([x, 1])
        na += 1
b = []
nb = 0
cur_b = a[0][0]
cur_n = a[0][1]
for i in range(1, na):
    while cur_n > 0 and cur_b < a[i][0]:
        t1 = cur_n // 2
        if cur_n % 2 > 0:
            b.append(cur_b)
        cur_b += 1
        cur_n = t1
    cur_b = a[i][0]
    cur_n += a[i][1]

while cur_n > 0:
    t1 = cur_n // 2
    if cur_n % 2 > 0:
        b.append(cur_b)
    cur_b += 1
    cur_n = t1

print b[len(b) - 1] + 1 - len(b)

