Solve the programming task below in a Python markdown code block.
Chef has a binary string S of size N. Chef can perform the following operation on the string:
Select any substring of size 3 and reverse it.

Find the minimum *distance* between any two 1s Chef can achieve, by applying the above operation any (possibly zero) number of times.

Note:
The *distance* between two characters S_{i} and S_{j} is defined as abs(i-j).
It is guaranteed that the string contains at least two occurrences of 1.
A substring is obtained by deleting some (possibly zero) elements from the beginning and some (possibly zero) elements from the end of the string.

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

- The first line of input will contain a single integer T, denoting the number of test cases.
- Each test case consists of multiple lines of input.
- The first line of each test case contains an integer N — the number of characters in the string.
- The next line contains a binary string of length N.

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

For each test case, output on a new line, the minimum distance between any two 1s Chef can achieve, by applying the above operation any (possibly zero) number of times.

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

$1 ≤ T ≤ 1000$
$2 ≤ N ≤ 10^{5}$
$S_{i}$ contains $0$ and $1$ only.
- It is guaranteed that $S$ contains at least two occurrences of $1$.
- The sum of $N$ over all test cases won't exceed $2\cdot 10^{5}$.

----- Sample Input 1 ------ 
3
2
11
3
101
7
0100101

----- Sample Output 1 ------ 
1
2
1
----- explanation 1 ------ 
Test case $1$: There are only two $1$s in the string. The distance between the $1$s is $2-1 = 1$.

Test case $2$: The distance between the given $1$s is $3-1 = 2$. It can be shown that we cannot achieve a distance smaller than $2$ by applying any number of operations.

Test case $3$: Chef can perform the following operation:
- Select the substring $S[2,4] = 100$ and reverse it. Thus, the string becomes $S = 0001101$. The minimum distance between the $1$s in the string is $5-4 = 1$. 

It can be shown that we cannot achieve a distance smaller than $1$ by applying any number of operations.