#include <bits/stdc++.h>
using namespace ::std;
bool cmp(int a, int b) { return a > b; }
int abs(int a) {
  if (a > 0) {
    return a;
  }
  return -a;
}
long long max(long long a, long long b) {
  if (a > b) {
    return a;
  }
  return b;
}
int a[100000];
int b[100000];
int main() {
  int n;
  while (cin >> n) {
    for (int i = 0; i < n; i++) {
      cin >> a[i];
    }
    int i = 1, j = 0;
    int tem = 1;
    if (n == 1) {
      b[j++] = a[0];
      tem = 0;
    }
    while (i < n) {
      while (i < n && a[i - 1] == a[i]) {
        i++;
        tem++;
      }
      if (i < n) {
        while (a[i - 1] != a[i] && tem) {
          if (tem % 2) {
            b[j++] = a[i - 1];
          }
          a[i - 1]++;
          tem /= 2;
        }
        tem++;
        i++;
      }
    }
    int ma = a[n - 1];
    while (tem) {
      if (tem % 2) {
        b[j++] = ma;
      }
      ma++;
      tem /= 2;
    }
    int result = b[0];
    for (i = 1; i < j; i++) {
      result += b[i] - b[i - 1] - 1;
    }
    cout << result << endl;
  }
  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;
bool cmp(int a, int b) { return a > b; }
int abs(int a) {
  if (a > 0) {
    return a;
  }
  return -a;
}
long long max(long long a, long long b) {
  if (a > b) {
    return a;
  }
  return b;
}
int a[100000];
int b[100000];
int main() {
  int n;
  while (cin >> n) {
    for (int i = 0; i < n; i++) {
      cin >> a[i];
    }
    int i = 1, j = 0;
    int tem = 1;
    if (n == 1) {
      b[j++] = a[0];
      tem = 0;
    }
    while (i < n) {
      while (i < n && a[i - 1] == a[i]) {
        i++;
        tem++;
      }
      if (i < n) {
        while (a[i - 1] != a[i] && tem) {
          if (tem % 2) {
            b[j++] = a[i - 1];
          }
          a[i - 1]++;
          tem /= 2;
        }
        tem++;
        i++;
      }
    }
    int ma = a[n - 1];
    while (tem) {
      if (tem % 2) {
        b[j++] = ma;
      }
      ma++;
      tem /= 2;
    }
    int result = b[0];
    for (i = 1; i < j; i++) {
      result += b[i] - b[i - 1] - 1;
    }
    cout << result << endl;
  }
  return 0;
}

```