#include <bits/stdc++.h>
using namespace std;
void add(map<int, bool> &c, int a) {
  if (!c[a]) {
    c[a] = true;
    return;
  }
  c[a] = false;
  add(c, a + 1);
}
void solve(istream &in, ostream &out) {
  int n;
  in >> n;
  map<int, bool> c;
  for (int i = 0; i < n; ++i) {
    int a;
    in >> a;
    add(c, a);
  }
  out << 1 + c.rbegin()->first -
             count_if(c.begin(), c.end(),
                      [](pair<int, bool> p) { return p.second; })
      << endl;
}
int main() {
  solve(cin, cout);
  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;
void add(map<int, bool> &c, int a) {
  if (!c[a]) {
    c[a] = true;
    return;
  }
  c[a] = false;
  add(c, a + 1);
}
void solve(istream &in, ostream &out) {
  int n;
  in >> n;
  map<int, bool> c;
  for (int i = 0; i < n; ++i) {
    int a;
    in >> a;
    add(c, a);
  }
  out << 1 + c.rbegin()->first -
             count_if(c.begin(), c.end(),
                      [](pair<int, bool> p) { return p.second; })
      << endl;
}
int main() {
  solve(cin, cout);
  return 0;
}

```