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

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