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
import sys
N=int(sys.stdin.readline().strip())
A=map(int, sys.stdin.readline().split())

def func(n):
    cnt=0
    while n%2==0:
        cnt+=1
        n/=2
    return cnt

ans=float("inf")
for x in A:
    ans=min(ans,func(x))
if ans==float("inf"):
    print 0
else:
    print ans
