#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:1000000000")
using namespace std;
const int size = 300010;
const long long alphabet = 130;
const long long INF = 1000000000000000000;
const int intINF = 1000000000;
const double pi = 4 * atan(1.0);
const long long MOD = 1000000007;
string conv(int n) {
  string res;
  while (n) {
    char c = n % 10 + '0';
    res += c;
    n /= 10;
  }
  return res;
}
map<int, int> q;
map<int, int>::iterator iter;
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%d", &x);
    q[x]++;
  }
  int cnt = 0;
  for (iter = q.begin(); iter != q.end(); iter++) {
    if (iter->second == 0) continue;
    if (iter->second == 1) {
      cnt++;
      continue;
    }
    int lol = iter->first;
    int val = iter->second;
    q[lol + 1] += val / 2;
    q[lol] -= val / 2 * 2;
    if (val & 1) cnt++;
  }
  int lol = (--q.end())->first;
  cout << lol - cnt + 1 << endl;
  return 0;
}

### Prompt

Please create a solution in CPP 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>
#pragma comment(linker, "/STACK:1000000000")
using namespace std;
const int size = 300010;
const long long alphabet = 130;
const long long INF = 1000000000000000000;
const int intINF = 1000000000;
const double pi = 4 * atan(1.0);
const long long MOD = 1000000007;
string conv(int n) {
  string res;
  while (n) {
    char c = n % 10 + '0';
    res += c;
    n /= 10;
  }
  return res;
}
map<int, int> q;
map<int, int>::iterator iter;
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%d", &x);
    q[x]++;
  }
  int cnt = 0;
  for (iter = q.begin(); iter != q.end(); iter++) {
    if (iter->second == 0) continue;
    if (iter->second == 1) {
      cnt++;
      continue;
    }
    int lol = iter->first;
    int val = iter->second;
    q[lol + 1] += val / 2;
    q[lol] -= val / 2 * 2;
    if (val & 1) cnt++;
  }
  int lol = (--q.end())->first;
  cout << lol - cnt + 1 << endl;
  return 0;
}

```