#include <bits/stdc++.h>
using namespace std;
const int mod = 1000000007;
const int MAX = 500000;
double eps = 1e-9;
const long long BIG_INF = 7000000000000000000LL;
const int INF = 2000000000;
double PI = 3.1415926535897932384626433832795;
string inttostring(int n) {
  stringstream a;
  a << n;
  string A;
  a >> A;
  return A;
}
int stringtoint(string A) {
  stringstream a;
  a << A;
  int p;
  a >> p;
  return p;
}
int main() {
  int n;
  cin >> n;
  int a;
  deque<int> D;
  for (int i = 0; i < n; i++) {
    cin >> a;
    D.push_back(a);
  }
  int f, maxb = 0, cnt = 0, bits = 0;
  while (!D.empty()) {
    f = D.front();
    cnt = 0;
    while (!D.empty() && f == D.front()) {
      cnt++;
      D.pop_front();
    }
    bits += (cnt % 2);
    maxb = max(maxb, f + 1);
    while (cnt >= 2) {
      D.push_front(f + 1);
      cnt -= 2;
    }
  }
  cout << maxb - bits << "\n";
}

### Prompt

Your challenge is to write 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;
const int mod = 1000000007;
const int MAX = 500000;
double eps = 1e-9;
const long long BIG_INF = 7000000000000000000LL;
const int INF = 2000000000;
double PI = 3.1415926535897932384626433832795;
string inttostring(int n) {
  stringstream a;
  a << n;
  string A;
  a >> A;
  return A;
}
int stringtoint(string A) {
  stringstream a;
  a << A;
  int p;
  a >> p;
  return p;
}
int main() {
  int n;
  cin >> n;
  int a;
  deque<int> D;
  for (int i = 0; i < n; i++) {
    cin >> a;
    D.push_back(a);
  }
  int f, maxb = 0, cnt = 0, bits = 0;
  while (!D.empty()) {
    f = D.front();
    cnt = 0;
    while (!D.empty() && f == D.front()) {
      cnt++;
      D.pop_front();
    }
    bits += (cnt % 2);
    maxb = max(maxb, f + 1);
    while (cnt >= 2) {
      D.push_front(f + 1);
      cnt -= 2;
    }
  }
  cout << maxb - bits << "\n";
}

```