#include <bits/stdc++.h>
using namespace std;
map<long long int, int> m;
int main() {
  int n;
  cin >> n;
  int arr[n];
  long long int max = -1;
  long long int count = 0;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
    if (m[arr[i]] == 0) {
      m[arr[i]]++;
      if (arr[i] > max) max = arr[i];
      count++;
    } else {
      long long int k = arr[i];
      while (m[k] != 0) {
        count--;
        m[k] = 0;
        k++;
      }
      m[k]++;
      count++;
      if (k > max) max = k;
    }
  }
  cout << max + 1 - count << endl;
  return 0;
}

### Prompt

Generate a CPP solution to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
map<long long int, int> m;
int main() {
  int n;
  cin >> n;
  int arr[n];
  long long int max = -1;
  long long int count = 0;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
    if (m[arr[i]] == 0) {
      m[arr[i]]++;
      if (arr[i] > max) max = arr[i];
      count++;
    } else {
      long long int k = arr[i];
      while (m[k] != 0) {
        count--;
        m[k] = 0;
        k++;
      }
      m[k]++;
      count++;
      if (k > max) max = k;
    }
  }
  cout << max + 1 - count << endl;
  return 0;
}

```