#include <bits/stdc++.h>
using namespace std;
map<long long, int> tree;
map<long long, int>::iterator iter;
int a;
long long s;
int z[120000];
void ins(long long aa) {
  iter = tree.find(aa);
  if (iter == tree.end()) {
    tree.insert(make_pair(aa, 0));
  } else {
    tree.erase(iter);
    ins(aa + 1);
  }
}
int main() {
  scanf("%d", &a);
  memset(z, 0, sizeof(z));
  for (int q = 0; q < a; q++) {
    scanf("%I64d", &s);
    ins(s);
  }
  iter = tree.end();
  iter--;
  printf("%I64d\n", (iter->first) + 1 - tree.size());
  return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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;
map<long long, int> tree;
map<long long, int>::iterator iter;
int a;
long long s;
int z[120000];
void ins(long long aa) {
  iter = tree.find(aa);
  if (iter == tree.end()) {
    tree.insert(make_pair(aa, 0));
  } else {
    tree.erase(iter);
    ins(aa + 1);
  }
}
int main() {
  scanf("%d", &a);
  memset(z, 0, sizeof(z));
  for (int q = 0; q < a; q++) {
    scanf("%I64d", &s);
    ins(s);
  }
  iter = tree.end();
  iter--;
  printf("%I64d\n", (iter->first) + 1 - tree.size());
  return 0;
}

```