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())
data = map(int, raw_input().split())
ans = 0
x = 0
carry = 0
ind = 0
def log2(c, base):
    #print c, base
    i = 0
    r = 0
    while c and i<base:
        if c%2 == 0:
            r += 1
        c /= 2
        i += 1
    #print c, r, base-i
    return c, r, base-i

while ind<n:
    now = data[ind]    
    tmpc = 0
    while ind<n and data[ind] == now:
        tmpc += 1
        ind += 1
    carry, q, p = log2(carry, now-x)
    ans += q + p
    x = now   
    carry += tmpc
    
carry, q, p = log2(carry, 2*10**9+1)
ans += q
print ans