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.
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, ans = 0;
  scanf("%d", &n);
  int arr[n];
  for (int i = (0); i < (n); ++i) scanf("%d", &arr[i]);
  map<int, int> M;
  for (int i = (0); i < (n); ++i) M[arr[i]]++;
  map<int, int>::iterator it;
  set<int> S;
  for (it = M.begin(); it != M.end(); ++it) {
    int rem = it->second % 2;
    int extra = it->second / 2;
    if (rem) S.insert(it->first);
    if (extra) M[it->first + 1] += extra;
  }
  set<int>::iterator ii;
  ans = *(S.rbegin()) + 1;
  for (ii = S.begin(); ii != S.end(); ++ii) ans--;
  printf("%d\n", ans);
  return 0;
}
