Student Numbers

To manage students efficiently, each student is assigned a unique student number. A student number is a string made only of digits from 0 to 9. All student numbers are different, and they all have the same length.

After assigning the numbers, assistant Jinyoung Kim wonders whether the numbers are longer than necessary. Suppose the following 7-digit student numbers are given.

In this case, the full 7 digits are not needed. If only the last three digits are kept, all student numbers are still distinguishable.

However, keeping fewer than three digits from the end cannot make all student numbers distinct.

Given the student numbers, find the smallest k such that keeping only the last k digits of each number still makes all student numbers distinct.

The first line contains the number of students N. (2 <= N <= 1,000)

Each of the next N lines contains one student number. All student numbers are different, have the same length, and consist only of digits from 0 to 9. The length of each student number is at most 100.

Print the smallest k such that keeping only the last k digits makes all student numbers distinct.