The Hamming distance between two strings $a$ and $b$ of equal length is the number of positions where the strings differ.

You are given $n$ bit strings, each of length $k$ and your task is to calculate the minimum Hamming distance between two strings.

The first input line has two integers $n$ and $k$ : the number of bit strings and their length.

Then there are $n$ lines each consisting of one bit string of length $k$ .

• $2 \le n \le 2 \cdot 10^4$
• $1 \le k \le 30$

Print the minimum Hamming distance between two strings.