*3 or /2

As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}. Snuke, an employee, would like to play with this sequence.

Specifically, he would like to repeat the following operation as many times as possible:

For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3". Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.

At most how many operations can be performed?

Constraints

• N is an integer between 1 and 10 \ 000 (inclusive).
• a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).

Input

Input is given from Standard Input in the following format:

N a_1 a_2 a_3 ... a_N

Output

Print the maximum number of operations that Snuke can perform.

Examples

Input

3 5 2 4

Output

3

Input

4 631 577 243 199

Output

0

Input

10 2184 2126 1721 1800 1024 2528 3360 1945 1280 1776

Output

39

inputFormat

Input

Input is given from Standard Input in the following format:

N a_1 a_2 a_3 ... a_N

outputFormat

Output

Print the maximum number of operations that Snuke can perform.

Examples

Input

3 5 2 4

Output

3

Input

4 631 577 243 199

Output

0

Input

10 2184 2126 1721 1800 1024 2528 3360 1945 1280 1776

Output

39

样例

10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776

39