#include <bits/stdc++.h>
using namespace std;
map<long long, bool> b;
map<long long, int> m;
long long n, a, y = 0, x = 0;
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a;
    m[a]++;
    if (b[a] == 0) {
      b[a] = 0;
      y++;
    }
    while (m[a] > 1) {
      m[a] = 0;
      y -= 2;
      b[a] = 0;
      a++;
      m[a]++;
      y++;
      b[a] = 1;
    }
    x = max(x, a);
  }
  x++;
  x -= y;
  cout << x;
  return 0;
}

### Prompt

Your task is to create 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, bool> b;
map<long long, int> m;
long long n, a, y = 0, x = 0;
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a;
    m[a]++;
    if (b[a] == 0) {
      b[a] = 0;
      y++;
    }
    while (m[a] > 1) {
      m[a] = 0;
      y -= 2;
      b[a] = 0;
      a++;
      m[a]++;
      y++;
      b[a] = 1;
    }
    x = max(x, a);
  }
  x++;
  x -= y;
  cout << x;
  return 0;
}

```