CF1791C.Prepend and Append

Timur initially had a binary string $^{\dagger}$ $s$ (possibly of length $0$ ). He performed the following operation several (possibly zero) times:

• Add $\texttt{0}$ to one end of the string and $\texttt{1}$ to the other end of the string. For example, starting from the string $\texttt{1011}$ , you can obtain either $\color{red}{\texttt{0}}\texttt{1011}\color{red}{\texttt{1}}$ or $\color{red}{\texttt{1}}\texttt{1011}\color{red}{\texttt{0}}$ .

You are given Timur's final string. What is the length of the shortest possible string he could have started with? $^{\dagger}$ A binary string is a string (possibly the empty string) whose characters are either $\texttt{0}$ or $\texttt{1}$ .

The first line of the input contains an integer $t$ ( $1 \leq t \leq 100$ ) — the number of testcases.

The first line of each test case contains an integer $n$ ( $1 \leq n \leq 2000$ ) — the length of Timur's final string.

The second line of each test case contains a string $s$ of length $n$ consisting of characters $\texttt{0}$ or $\texttt{1}$ , denoting the final string.

For each test case, output a single nonnegative integer — the shortest possible length of Timur's original string. Note that Timur's original string could have been empty, in which case you should output $0$ .

In the first test case, the shortest possible string Timur started with is $\texttt{0}$ , and he performed the following operation: $\texttt{0} \to \color{red}{\texttt{1}}\texttt{0}\color{red}{\texttt{0}}$ .

In the second test case, the shortest possible string Timur started with is $\texttt{11}$ , and he performed the following operation: $\texttt{11} \to \color{red}{\texttt{0}}\texttt{11}\color{red}{\texttt{1}}$ .

In the third test case, the shortest possible string Timur started with is $\texttt{10101}$ , and he didn't perform any operations.

In the fourth test case, the shortest possible string Timur started with is the empty string (which we denote by $\varepsilon$ ), and he performed the following operations: $\varepsilon \to \color{red}{\texttt{1}}\texttt{}\color{red}{\texttt{0}} \to \color{red}{\texttt{0}}\texttt{10}\color{red}{\texttt{1}} \to \color{red}{\texttt{1}}\texttt{0101}\color{red}{\texttt{0}}$ .

In the fifth test case, the shortest possible string Timur started with is $\texttt{101}$ , and he performed the following operations: $\texttt{101} \to \color{red}{\texttt{0}}\texttt{101}\color{red}{\texttt{1}} \to \color{red}{\texttt{1}}\texttt{01011}\color{red}{\texttt{0}}$ .