Score : $200$ points

Problem Statement

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.

3
8 12 40

2

Initially, $[8, 12, 40]$ are written on the blackboard. Since all those integers are even, Snuke can perform the operation.

After the operation is performed once, $[4, 6, 20]$ are written on the blackboard. Since all those integers are again even, he can perform the operation.

After the operation is performed twice, $[2, 3, 10]$ are written on the blackboard. Now, there is an odd number $3$ on the blackboard, so he cannot perform the operation any more.

Thus, Snuke can perform the operation at most twice.

4
5 6 8 10

0

Since there is an odd number $5$ on the blackboard already in the beginning, Snuke cannot perform the operation at all.

6
382253568 723152896 37802240 379425024 404894720 471526144

8