Solve the programming task below in a Python markdown code block.
You are given a binary string S of length N. You are allowed to perform the following types of operations on string S:
Delete any one character from S, and concatenate the remaining parts of the string. For example, if we delete the third character of S = 1101, it becomes S = 111.
Flip all the characters of S. For example, if we flip all character of S = 1101, it becomes S = 0010.

Given that you can use either type of operation any number of times, find the minimum number of operations required to make all characters of the string S equal to 0.

------ 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 length of the string.
- The next line contains a binary string S of length N.

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

For each test case, output on a new line, the minimum number of operations required to make all characters of the string S equal to 0.

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

$1 ≤ T ≤ 2000$
$1 ≤ N ≤ 10^{5}$
$S$ contains $0$ and $1$ only.
- The sum of $N$ over all test cases won't exceed $2\cdot 10^{5}$.

----- Sample Input 1 ------ 
4
2
01
3
101
3
111
4
0000

----- Sample Output 1 ------ 
1
2
1
0

----- explanation 1 ------ 
Test case $1$: You can use one operation to delete the second character of the string $S$. Thus, the string becomes $0$. Note that all characters of this string are $0$ and thus, it satisfies the conditions.

Test case $2$: You can perform the following operations:
- Operation $1$: Flip all characters of the string. Thus, string becomes $010$.
- Operation $2$: Delete the second character of the string. Thus, string becomes $00$.

Note that we have obtained a string having all characters as $0$ in two operations. It can be shown that this is the minimum number of operations required.

Test case $3$: You can use one operation to flip all characters of the string $S$. Thus, the string becomes $000$. Note that all characters of this string are $0$ and thus, it satisfies the conditions.

Test case $4$: The existing string satisfies the conditions. Thus, we require zero operations.