Minimum Hamming Distance

Given n bit-strings, you are asked to find the pair of bit-strings that has the minimum hamming distance.

Input

The first line of the input contains a single integer n (2 ≤ n ≤ 1000).

The next n lines contain bit-strings of the same length each on a separate line (1 ≤ || ≤ 30).

Output

The program should print the minimum hamming distance of those pairs.

Examples

Explanation

The hamming distance between 1011 and 1010 is 1.