Bear and Steady Gene

A gene is represented as a string of length (where is divisible by ), composed of the letters , , , and . It is considered to be steady if each of the four letters occurs exactly times. For example, and are both steady genes.

Bear Limak is a famous biotechnology scientist who specializes in modifying bear DNA to make it steady. Right now, he is examining a gene represented as a string . It is not necessarily steady. Fortunately, Limak can choose one (maybe empty) substring of and replace it with any string of the same length.

Modifying a large substring of bear genes can be dangerous. Given a string , can you help Limak find the length of the smallest possible substring that he can replace to make a steady gene?

Note: A substring of a string is a subsequence made up of zero or more contiguous characters of .

As an example, consider . The substring just before or after can be replaced with or . One selection would create .

Function Description

Complete the function in the editor below. It should return an integer that represents the length of the smallest substring to replace.

steadyGene has the following parameter:

gene: a string

Input Format

The first line contains an interger divisible by , that denotes the length of a string .
The second line contains a string of length .

Constraints

is divisible by

Subtask

in tests worth points.

Output Format

Print the length of the minimum length substring that can be replaced to make stable.

Sample Input

8  
GAAATAAA

Sample Output

Explanation

One optimal solution is to replace with resulting in .
The replaced substring has length .