Shift only

There are N positive integers written on a blackboard: A_1, ..., A_N.

Snuke can perform the following operation when all integers on the blackboard are even:

• Replace each integer X on the blackboard by X divided by 2.

Find the maximum possible number of operations that Snuke can perform.

Constraints

• 1 \leq N \leq 200
• 1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_N

Output

Print the maximum possible number of operations that Snuke can perform.

Examples

Input

3 8 12 40

Output

2

Input

4 5 6 8 10

Output

0

Input

6 382253568 723152896 37802240 379425024 404894720 471526144

Output

8

inputFormat

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_N

outputFormat

Output

Print the maximum possible number of operations that Snuke can perform.

Examples

Input

3 8 12 40

Output

2

Input

4 5 6 8 10

Output

0

Input

6 382253568 723152896 37802240 379425024 404894720 471526144

Output

8

样例

6
382253568 723152896 37802240 379425024 404894720 471526144

8