#include <bits/stdc++.h>
using namespace std;
map<int, int> t;
map<int, int>::iterator it;
int a, b, c, d, e, f, g, h, i, j, k, m, n;
void deal() {
  t.clear();
  scanf("%d", &n);
  for (i = 1; i <= n; i++) {
    scanf("%d", &a);
    while ((it = t.find(a)) != t.end()) {
      t.erase(it);
      a++;
    }
    t[a] = 1;
  }
  g = t.size();
  it = t.end();
  it--;
  h = it->first;
  printf("%d\n", h - g + 1);
}
int main() {
  deal();
  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<int, int> t;
map<int, int>::iterator it;
int a, b, c, d, e, f, g, h, i, j, k, m, n;
void deal() {
  t.clear();
  scanf("%d", &n);
  for (i = 1; i <= n; i++) {
    scanf("%d", &a);
    while ((it = t.find(a)) != t.end()) {
      t.erase(it);
      a++;
    }
    t[a] = 1;
  }
  g = t.size();
  it = t.end();
  it--;
  h = it->first;
  printf("%d\n", h - g + 1);
}
int main() {
  deal();
  return 0;
}

```