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.
from sys import stdin, stdout

inputIdx = 0;
input = stdin.read().strip().split();

def nextToken():
  global inputIdx, input;
  token = input[inputIdx];
  inputIdx += 1;
  return token;

def main():
  global inputIdx, input;
  while inputIdx < len(input):
    n = int( nextToken() );
    arr = [ int( nextToken() ) for i in range(n) ];
    diff = 0;
    cur = -1; cnt = 0;
    i = 0;
    ans = max(arr);
    while i < n or cur != -1:
      ans = max( ans, cur );
      if ( i < n and cur != -1 and arr[i] == cur ) or ( cur == -1 ):
        j = i;
        while j < n and arr[i] == arr[j]:
          j += 1;
        cnt += j-i;
        cur = arr[i];
        i = j;
      if (cnt&1) == 1:
        diff += 1;
      cur += 1;
      cnt //= 2;
      if cnt == 0:
        cur = -1;
    ans -= diff-1;
    print( int(ans) );

main();
