#include <bits/stdc++.h>
using namespace std;
const double pi = acos(-1.0);
int n;
priority_queue<int, vector<int>, greater<int> > P;
void solve() {
  vector<int> p;
  while (!P.empty()) {
    int x = P.top();
    P.pop();
    if (!P.empty()) {
      int y = P.top();
      if (x == y) {
        P.pop();
        P.push(x + 1);
      } else {
        p.push_back(x);
      }
    } else {
      p.push_back(x);
    }
  }
  cout << (p.back() - (int)p.size() + 1) << endl;
}
int main() {
  while (cin >> n) {
    for (int i = 0; i < n; i++) {
      int a;
      scanf("%d", &a);
      P.push(a);
    }
    solve();
  }
}

### 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;
const double pi = acos(-1.0);
int n;
priority_queue<int, vector<int>, greater<int> > P;
void solve() {
  vector<int> p;
  while (!P.empty()) {
    int x = P.top();
    P.pop();
    if (!P.empty()) {
      int y = P.top();
      if (x == y) {
        P.pop();
        P.push(x + 1);
      } else {
        p.push_back(x);
      }
    } else {
      p.push_back(x);
    }
  }
  cout << (p.back() - (int)p.size() + 1) << endl;
}
int main() {
  while (cin >> n) {
    for (int i = 0; i < n; i++) {
      int a;
      scanf("%d", &a);
      P.push(a);
    }
    solve();
  }
}

```