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 ara[2 * 100007];
int main() {
  int t, tst = 1;
  int n;
  scanf("%d", &n);
  map<int, int> mp;
  for (int i = 0; i < (n); i++) {
    scanf("%d", &ara[i]);
    mp[ara[i]]++;
  }
  for (auto it = mp.begin(); it != mp.end(); it++) {
    if (it->second / 2 != 0) {
      mp[it->first + 1] += it->second / 2;
      it->second -= (it->second / 2) * 2;
    }
  }
  int prev = -1, ans = 0;
  for (pair<int, int> x : mp) {
    if (x.second != 0) {
      ans += x.first - prev - 1;
      prev = x.first;
    }
  }
  printf("%d\n", ans);
  return 0;
}
