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

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 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.