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.
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, ctr;
  vector<int> num, ans;
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d", &ctr);
    num.push_back(ctr);
  }
  sort(num.begin(), num.end());
  ctr = 1;
  int tmp, x, id;
  for (int i = 1; i < n; ++i) {
    if (num[i] != num[i - 1]) {
      tmp = ctr;
      x = num[i - 1];
      id = i;
      while (tmp > 0) {
        if (x == num[id]) {
          for (; id <= n; ++id) {
            if (id == n) break;
            if (num[id] != x) break;
            tmp++;
          }
        }
        if (tmp % 2 == 1) ans.push_back(x);
        x++;
        tmp /= 2;
      }
      i = id;
      if (i < n)
        ctr = 1;
      else
        ctr = 0;
    } else
      ctr++;
  }
  x = num[n - 1];
  while (ctr > 0) {
    if (ctr % 2 == 1) ans.push_back(x);
    x++;
    ctr /= 2;
  }
  sort(ans.begin(), ans.end());
  long long ret = ans[0] - 0;
  for (int i = 1; i < ans.size(); ++i) {
    ret += (ans[i] - ans[i - 1] - 1);
  }
  cout << ret << endl;
  return 0;
}
