You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
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 $$$\color{red}{\texttt{1}}\texttt{1011}\color{red}{\texttt{0}}$$$.

$$$^{\dagger}$$$ A binary string is a string (possibly the empty string) whose characters are either $$$\texttt{0}$$$ or $$$\texttt{1}$$$.

## Input Format
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.

## Output Format
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 $$$0$$$.

## Examples
```input
9
3
100
4
0111
5
10101
6
101010
7
1010110
1
1
2
10
2
11
10
1011011010
```
```output
1
2
5
0
3
1
0
2
4
```

## Note
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: $$$\texttt{101} \to \color{red}{\texttt{0}}\texttt{101}\color{red}{\texttt{1}} \to \color{red}{\texttt{1}}\texttt{01011}\color{red}{\texttt{0}}$$$.

Now solve the problem and return the code.