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;
const double pi = acos(-1.0);
const double eps = 1e-8;
vector<string> parse(string s, string c) {
  int len = c.length(), p = -len, np;
  vector<string> ans;
  do {
    np = s.find(c, p + len);
    ans.push_back(s.substr(p + len, np - p - len));
    p = np;
  } while (p != string::npos);
  return ans;
}
set<long long> input;
map<long long, int> cont;
set<long long> ones;
int main() {
  ios_base::sync_with_stdio(false);
  int n;
  long long x;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> x;
    cont[x]++;
    input.insert(x);
  }
  int curr_cont = 0;
  set<long long>::iterator it;
  for (it = input.begin(); it != input.end(); it++) {
    long long curr_ele = *it;
    curr_cont = cont[curr_ele];
    if (curr_cont & 1) ones.insert(curr_ele);
    int carry = curr_cont / 2;
    if (carry > 0) {
      input.insert(curr_ele + 1);
      cont[curr_ele + 1] += carry;
    }
  }
  long long aval = ones.size();
  it = input.end();
  it--;
  long long mx = *it;
  cout << mx + 1 - aval << endl;
  return 0;
}
