#include <bits/stdc++.h>
using namespace std;
set<long long> sset;
void add(int n) {
  set<long long>::iterator it = sset.find(n);
  if (it == sset.end()) {
    sset.insert(n);
  } else {
    sset.erase(it);
    add(n + 1);
  }
}
int main() {
  cin.sync_with_stdio(false);
  int n;
  cin >> n;
  while (n--) {
    int t;
    cin >> t;
    add(t);
  }
  set<long long>::iterator it = sset.end();
  it--;
  cout << *it - sset.size() + 1 << endl;
}

### Prompt

Please formulate 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;
set<long long> sset;
void add(int n) {
  set<long long>::iterator it = sset.find(n);
  if (it == sset.end()) {
    sset.insert(n);
  } else {
    sset.erase(it);
    add(n + 1);
  }
}
int main() {
  cin.sync_with_stdio(false);
  int n;
  cin >> n;
  while (n--) {
    int t;
    cin >> t;
    add(t);
  }
  set<long long>::iterator it = sset.end();
  it--;
  cout << *it - sset.size() + 1 << endl;
}

```