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() {
  map<int, int> a;
  int n, num;
  scanf("%d", &n);
  for (int i = (int)0; i < (int)n; ++i) {
    scanf("%d", &num);
    a[num]++;
  }
  int count = 0, last;
  for (typeof(a.begin()) i = a.begin(); i != a.end(); i++) {
    count += i->second % 2;
    last = i->first;
    if (i->second > 1) a[i->first + 1] += i->second / 2;
  }
  cout << last - count + 1 << "\n";
  return 0;
}
