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 main() {
  int j, i, z = 0, n, a[100005], cnt = 0, s = 0, mx = -1;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  while (z < n) {
    i = z;
    int rep = 1 + cnt;
    for (j = i + 1; j < n; j++)
      if (i != j && a[j] == a[i])
        rep++, i = j;
      else if (a[j] > a[i])
        break;
    if (rep & 1) s++, z++, mx = max(mx, a[i]);
    cnt = rep / 2;
    z += cnt;
    for (; cnt > 0; i--, cnt--) a[i]++;
  }
  cout << mx - s + 1 << endl;
  return 0;
}
