Solve the programming task below in a Python markdown code block.
A gene is represented as a string of length $n$ (where $n$ is divisible by $4$), composed of the letters $\mbox{A}$, $\mbox{C}$, $\textbf{T}$, and $\mbox{G}$.
It is considered to be steady if each of the four letters occurs exactly $\frac{n}{4}$ times.  For example, $\textbf{GACT}$ and $\textbf{AAGTGCCT}$ 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 $\textit{gene}$.  It is not necessarily steady.  Fortunately, Limak can choose one (maybe empty) substring of $\textit{gene}$ and replace it with any string of the same length.

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

Note: A substring of a string $\boldsymbol{\mathrm{~S~}}$ is a subsequence made up of zero or more contiguous characters of $\boldsymbol{\mathrm{~S~}}$.

As an example, consider $\textit{gene}=\textit{ACTGAAAG}$.  The substring $\boldsymbol{AA}$ just before or after $\mbox{G}$ can be replaced with $\textit{CT}$ or $\boldsymbol{TC}$.  One selection would create $\textbf{ACTGACTG}$.

Function Description

Complete the $\textit{steadyGene}$ 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 $n$ divisible by $4$, that denotes the length of a string $\textit{gene}$. 

The second line contains a string $\textit{gene}$ of length $n$.

Constraints

$4\leq n\leq500000$  
$n$ is divisible by $4$  
$gene[i]\in[CGAT]$  

Subtask  

$4\leq n\leq2000$ in tests worth $30\%$ points.

Output Format

Print the length of the minimum length substring that can be replaced to make $\textit{gene}$ stable.

Sample Input
8  
GAAATAAA

Sample Output
5

Explanation

One optimal solution is to replace $\textbf{AAATA}$ with $\textbf{TTCCG}$ resulting in $\textbf{GTTCCGAA}$. 

The replaced substring has length $5$.