Hamming Distance

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.

Input

The first line has two integers $n(2\le n\le 2\cdot 10^4)$ and $k(1\le k\le 30)$: the number of bit strings and their length.

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

Output

Print the minimum Hamming distance between two strings.

Examples