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
#!/usr/bin/python

import sys

def main(argv):
    line = sys.stdin.readline()
    while line:
        N = line.rstrip("\n")
        A = map(lambda a: int(a), sys.stdin.readline().rstrip("\n").split(" "))
        count = 0
        flag = True
        while flag:
            for i in xrange(len(A)):
                if A[i] % 2 != 0:
                    flag = False
                    break
                A[i] = A[i] / 2
            else:
                count += 1
        print count

        line = sys.stdin.readline()

if __name__ == "__main__":
    main(sys.argv)