#include <algorithm>
#include <cassert>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>

using namespace std;

#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) FOR(i, 0, n)
#define TRACE(x) cout << #x << " = " << x << endl
#define _ << " _ " <<

typedef long long llint;

int main(void) {
  int n;
  scanf("%d", &n);

  int active = 0;
  int ret = 0;
  
  REP(i, n) {
    int x;
    scanf("%d", &x);

    int pw = (x & (x - 1)) == 0;
    int k = 0;
    while (x > 1) {
      x = (x + 1) / 2;
      k++;
    }
    
    if (pw) {
      if (k > active) {
        ret += k - active;
      }
      active = k;
    } else {
      if (active >= k) {
        active = k - 1;
      } else {
        ret += k - active;
        active = k;
      }
    }
  }
  
  printf("%d\n", ret);
  return 0;
}

### Prompt

Your challenge is to write a Cpp solution to the following problem:

There are A slimes lining up in a row. Initially, the sizes of the slimes are all 1.

Snuke can repeatedly perform the following operation.

* Choose a positive even number M. Then, select M consecutive slimes and form M / 2 pairs from those slimes as follows: pair the 1-st and 2-nd of them from the left, the 3-rd and 4-th of them, ..., the (M-1)-th and M-th of them. Combine each pair of slimes into one larger slime. Here, the size of a combined slime is the sum of the individual slimes before combination. The order of the M / 2 combined slimes remain the same as the M / 2 pairs of slimes before combination.



Snuke wants to get to the situation where there are exactly N slimes, and the size of the i-th (1 ≤ i ≤ N) slime from the left is a_i. Find the minimum number of operations required to achieve his goal.

Note that A is not directly given as input. Assume A = a_1 + a_2 + ... + a_N.

Constraints

* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9

Input

Input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print the minimum number of operations required to achieve Snuke's goal.

Examples

Input

2
3 3


Output

2


Input

4
2 1 2 2


Output

2


Input

1
1


Output

0


Input

10
3 1 4 1 5 9 2 6 5 3


Output

10

### Response

```cpp
#include <algorithm>
#include <cassert>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>

using namespace std;

#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) FOR(i, 0, n)
#define TRACE(x) cout << #x << " = " << x << endl
#define _ << " _ " <<

typedef long long llint;

int main(void) {
  int n;
  scanf("%d", &n);

  int active = 0;
  int ret = 0;
  
  REP(i, n) {
    int x;
    scanf("%d", &x);

    int pw = (x & (x - 1)) == 0;
    int k = 0;
    while (x > 1) {
      x = (x + 1) / 2;
      k++;
    }
    
    if (pw) {
      if (k > active) {
        ret += k - active;
      }
      active = k;
    } else {
      if (active >= k) {
        active = k - 1;
      } else {
        ret += k - active;
        active = k;
      }
    }
  }
  
  printf("%d\n", ret);
  return 0;
}

```