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 n, m, i, j, l, mn, t, c[101010], r;
set<unsigned int> q;
map<unsigned int, int> u;
unsigned int k, x, pr;
int main() {
  l = 499999, r = 500000;
  cin >> n;
  c[1] = 0;
  for (i = 2; i <= n; i++) {
    c[i] = c[i - 1];
    if (1 << (c[i] + 1) == i) c[i]++;
  }
  for (i = 1; i <= n; i++) {
    scanf("%d", &t);
    u[t]++;
    q.insert(t);
  }
  pr = 0;
  while (!q.empty()) {
    x = *q.begin();
    q.erase(q.begin());
    if (x != pr) {
      k += x - pr;
    }
    pr = x + 1;
    t = u[x];
    for (i = c[t]; i >= 1; i--) {
      if (t & (1 << i)) {
        u[x + i]++;
        q.insert(x + i);
      }
    }
    if (!(t & 1)) {
      k++;
    }
  }
  cout << k;
  return 0;
}
