Roger has found ~N~ numbers, numbered ~A_1, A_2, \dots, A_N~. Roger wants to know how many digits there are in the binary representation of the product ~A_1 \times A_2 \times \dots \times A_N~. Help Roger find this number!

Input Specification

The first line will consist of a single integer, ~N~.
The next line will consist of ~N~ space separated integers, ~A_1, A_2, \dots, A_N~.

Output Specification

Print the number of digits in the binary representation of the product ~A_1 \times A_2 \times \dots \times A_N~.

Constraints

Subtask 1 [10%]

~1 \le N \le 10~

~1 \le A_i \le 10~

Subtask 2 [90%]

~1 \le N \le 10^5~

~1 \le A_i \le 10^{18}~

Sample Input

5
2 2 2 2 2

Sample Output

6

Explanation of Sample Output

Let ~X_{dec}~ denote a decimal number and ~X_{bin}~ denote a binary number. ~2_{dec} \times 2_{dec} \times 2_{dec} \times 2_{dec} \times 2_{dec} = 32_{dec} = 100000_{bin}~.