github.com/captn3m0/codechef.git

---
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---
### Read problems statements in [Mandarin Chinese](https://www.codechef.com/download/translated/COOK130/mandarin/BNSONSTR.pdf), [Russian](https://www.codechef.com/download/translated/COOK130/russian/BNSONSTR.pdf), [Vietnamese](https://www.codechef.com/download/translated/COOK130/vietnamese/BNSONSTR.pdf) and [Bengali](https://www.codechef.com/download/translated/COOK130/bengali/BNSONSTR.pdf) as well.

A circular binary string is called *good* if it contains at least one character '1' and there is an integer $d$ such that for each character '1', the distance to the nearest character '1' clockwise is $d$.

You are given a circular binary string $S$ with length $N$. You may choose some characters in this string and flip them (i.e. change '1' to '0' or vice versa). Convert the given string into a good string by flipping the smallest possible number of characters.

### Input
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- The second line contains a single string $S$ with length $N$.

### Output
Print a single line containing one integer ― the minimum number of flips required to transform the initial string into a good string.

### Constraints
- $1 \leq T \leq 100$
- $1 \leq N \leq 5 \cdot 10^5$
- $S$ contains only characters '0' and '1'
- the sum of $N$ over all test cases does not exceed $5 \cdot 10^5$

### Example Input
```
2
6
110011
4
0001
```

### Example Output
```
2
0
```

<aside style='background: #f8f8f8;padding: 10px 15px;'><div>All submissions for this problem are available.</div></aside>