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

DBG_FLAG = 1

def pdbg(str):
    if(DBG_FLAG == 1):
        sys.stdout.flush()
        print str

def max_num(num):
    if(num % 2):
        return 0
    else:
        return 1 + max_num(num / 2)

# get num
N = int(raw_input())
array = map(int, raw_input().split())

#pdbg(N)
#pdbg(array)

min = 1
num = 0

ans = []

for item in array:
    ans.append(max_num(item))

ans.sort()

print ans[0]
