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 key;
  Node *left, *pre;
};
int main() {
  Node *head = new Node;
  head->key = -1;
  Node *tah = head;
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    tah->left = new Node;
    Node *now = tah->left;
    now->key = a;
    now->pre = tah;
    now->left = NULL;
    tah = now;
  }
  Node *now = head;
  while (now->left != NULL) {
    Node *rep = now;
    while (rep->left != NULL && now->key == rep->left->key) rep = rep->left;
    if (now == rep) {
      now = now->left;
      continue;
    }
    while (rep != now && rep->left != now) {
      Node *s2 = rep;
      Node *s1 = rep->pre;
      s1->key++;
      s1->left = s2->left;
      if (s2->left != NULL) s2->left->pre = s1;
      delete s2;
      rep = s1->pre;
    }
  }
  now = head;
  int len = 0;
  while (now->left != NULL) {
    now = now->left;
    len++;
  }
  cout << now->key - len + 1 << endl;
}
