Solve the programming task below in a Python markdown code block.
A binary string is called *alternating* if no two adjacent characters of the string are equal. Formally, a binary string T of length M is called alternating if T_{i} \neq T_{i +1} for each 1 ≤ i < M. 

For example, 0, 1, 01, 10, 101, 010, 1010 are alternating strings while 11, 001, 1110 are not.

You are given a binary string S of length N. You would like to rearrange the characters of S such that the length of the longest alternating substring of S is maximum. Find this maximum value.

A binary string is a string that consists of characters 0 and 1. A string a is a [substring] of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end.

------ Input Format ------ 

- The first line of input contains an integer T, denoting the number of test cases. The T test cases then follow:
- The first line of each test case contains an integer N.
- The second line of each test case contains the binary string S.

------ Output Format ------ 

For each test case, output the maximum possible length of the longest alternating substring of S after rearrangement.

------ Constraints ------ 

$1 ≤ T ≤ 10^{4}$
$1 ≤ N ≤ 10^{5}$
$S$ contains only the characters 0 and 1.
- Sum of $N$ over all test cases does not exceed $2 \cdot 10^{5}$.

----- Sample Input 1 ------ 
4
3
110
4
1010
4
0000
7
1101101

----- Sample Output 1 ------ 
3
4
1
5

----- explanation 1 ------ 
Test case $1$: Swapping the second and third characters makes $S=101$. Hence the length of the longest alternating substring is $3$ (choosing the entire string as a substring).

Test case $2$: The given string $S=1010$ is an alternating string of length $4$.

Test case $3$: The length of the longest alternating substring is $1$ for any rearrangement of  $S=0000$.

Test case $4$: One possible rearrangement of $S$ is $1\underline{10101}1$, which has an alternating substring of length $5$ (the substring starting at index $2$ and ending at index $6$).