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>
int i, j, n, x, sum = 0, t = 0, total = 0;
int main() {
  while (scanf("%d", &n) != EOF) {
    for (i = 1; i <= n; i++) {
      scanf("%d", &x);
      if (x != t) {
        while (total != 0 && t < x) {
          if (total % 2 != 1) sum++;
          total = total / 2;
          t++;
        }
        sum = sum + x - t;
        t = x;
      }
      total++;
    }
    while (total != 0) {
      if (total % 2 != 1) sum++;
      total = total / 2;
    }
    printf("%d\n", sum);
  }
  return 0;
}
