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;
map<long long, int> mark;
int32_t main() {
  int n;
  scanf("%d", &n);
  set<long long> s;
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%d", &x);
    mark[x]++;
    s.insert(x);
  }
  int p = 0;
  long long MX = 0;
  while (s.size()) {
    long long u = *s.begin();
    ((MX) = max((MX), (u)));
    mark[u + 1] += mark[u] / 2;
    if (mark[u + 1]) s.insert(u + 1);
    if (mark[u] % 2) p--;
    s.erase(s.begin());
  }
  return cout << MX + p + 1 << endl, 0;
}
