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.
class BinNumber:
  bits = {}
  def Set(self, pow):
    k = pow
    while k in self.bits and self.bits[k] == 1:
      self.bits[k] = 0
      k += 1
    self.bits[k] = 1
  def Add(self, pow, times):
    i = 0
    while (1 << i) <= times:
      if times & (1 << i):
        self.Set(pow + i)
      i += 1
  def GetMaxBit(self):
    return max(self.bits.keys())
  def GetSettedBitsCount(self):
    return sum(self.bits.values())
  def GetZeroCount(self):
    return self.GetMaxBit() - self.GetSettedBitsCount() + 1
    
input()
count = {}
for i in map(int, raw_input().split()):
  if not i in count:
    count[i] = 1
  else:
    count[i] += 1
n = BinNumber()
for num in count.keys():
  n.Add(num, count[num])
print n.GetZeroCount()