**Time limit:**1.00 s**Memory limit:**512 MB

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 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 $k$.

**Output**

Print the minimum Hamming distance between two strings.

**Constraints**

- $2 \le n \le 2 \cdot 10^4$

- $1 \le k \le 30$

**Example**

Input:

`5 6`

110111

001000

100001

101000

101110

Output:

`1`

Explanation: The strings

`101000`

and `001000`

differ only at the first position.