#include <bits/stdc++.h>
using namespace std;
long long a[100005];
map<long long, long long> mp;
set<long long> st;
int main() {
  int n;
  long long mx = 0, cnt = 0;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%I64d", &a[i]);
    st.insert(a[i]);
    mp[a[i]]++;
  }
  for (set<long long>::iterator it = st.begin(); it != st.end(); it++) {
    if (mp[*it] >= 2) {
      long long x = mp[*it] / 2;
      mp[*it] -= 2 * x;
      mp[*it + 1] += x;
      st.insert(*it + 1);
    }
    if (mp[*it] > 0) cnt++;
    mx = *it;
  }
  printf("%I64d\n", mx + 1 - cnt);
  return 0;
}

### Prompt

In Cpp, your task is to solve 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;
long long a[100005];
map<long long, long long> mp;
set<long long> st;
int main() {
  int n;
  long long mx = 0, cnt = 0;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%I64d", &a[i]);
    st.insert(a[i]);
    mp[a[i]]++;
  }
  for (set<long long>::iterator it = st.begin(); it != st.end(); it++) {
    if (mp[*it] >= 2) {
      long long x = mp[*it] / 2;
      mp[*it] -= 2 * x;
      mp[*it + 1] += x;
      st.insert(*it + 1);
    }
    if (mp[*it] > 0) cnt++;
    mx = *it;
  }
  printf("%I64d\n", mx + 1 - cnt);
  return 0;
}

```