Squeezing Slimes

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

inputFormat

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

outputFormat

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

样例

10
3 1 4 1 5 9 2 6 5 3

10