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;
struct node {
  int x;
  node(int xx) { x = xx; }
};
bool operator<(node const &a, node const &b) {
  if (a.x > b.x)
    return true;
  else
    return false;
}
priority_queue<node> p;
int main() {
  int n;
  scanf("%d", &n);
  int tmp;
  for (int i = 0; i < n; i++) {
    scanf("%d", &tmp);
    p.push(node(tmp));
  }
  int cnt = -1;
  int ans = 0;
  node ntmp(0);
  node nttmp(0);
  while (!p.empty()) {
    ntmp = p.top();
    p.pop();
    if (!p.empty())
      nttmp = p.top();
    else
      nttmp.x = -1;
    if (nttmp.x == ntmp.x) {
      p.pop();
      p.push(node(ntmp.x + 1));
      continue;
    }
    ans += ntmp.x - cnt - 1;
    cnt = ntmp.x;
  }
  printf("%d\n", ans);
  return 0;
}
