#include <bits/stdc++.h>
using namespace std;
map<int, bool> bits;
int n, a;
void add(int k) {
  if (bits[k]) {
    bits[k] = false;
    add(k + 1);
  } else {
    bits[k] = true;
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  while (n--) {
    cin >> a;
    add(a);
  }
  int num = 0, ma = 0;
  for (pair<int, bool> p : bits) {
    if (p.second) {
      ++num;
      ma = max(ma, p.first);
    }
  }
  cout << ma + 1 - num << endl;
  return 0;
}

### Prompt

Please create a solution in cpp 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<int, bool> bits;
int n, a;
void add(int k) {
  if (bits[k]) {
    bits[k] = false;
    add(k + 1);
  } else {
    bits[k] = true;
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  while (n--) {
    cin >> a;
    add(a);
  }
  int num = 0, ma = 0;
  for (pair<int, bool> p : bits) {
    if (p.second) {
      ++num;
      ma = max(ma, p.first);
    }
  }
  cout << ma + 1 - num << endl;
  return 0;
}

```