#include <cstdio>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <cctype>
#include <algorithm>
#define R register
#define IN inline
#define W while
#define gc getchar()
#define MX 100050
#define ll long long
template <class T>
IN void in(T &x)
{
	x = 0; R char c = gc;
	W (!isdigit(c)) c = gc;
	W (isdigit(c))
	x = (x << 1) + (x << 3) + c - 48, c = gc;
}
int main(void)
{
	int num, buf, mul; in(num);
	bool merge = false; ll ans = 0, cut = 0;
	W (num--)
	{
		in(buf); mul = std::log2(buf); merge = false;
		if((1 << mul) != buf) merge = true;
		if(cut < mul) ans += mul - cut;
		if(cut > mul) merge = false;
		cut = mul; if(merge) ++cut, ++ans;
	}
	printf("%lld", ans);
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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 <cstdio>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <cctype>
#include <algorithm>
#define R register
#define IN inline
#define W while
#define gc getchar()
#define MX 100050
#define ll long long
template <class T>
IN void in(T &x)
{
	x = 0; R char c = gc;
	W (!isdigit(c)) c = gc;
	W (isdigit(c))
	x = (x << 1) + (x << 3) + c - 48, c = gc;
}
int main(void)
{
	int num, buf, mul; in(num);
	bool merge = false; ll ans = 0, cut = 0;
	W (num--)
	{
		in(buf); mul = std::log2(buf); merge = false;
		if((1 << mul) != buf) merge = true;
		if(cut < mul) ans += mul - cut;
		if(cut > mul) merge = false;
		cut = mul; if(merge) ++cut, ++ans;
	}
	printf("%lld", ans);
}

```