You are given a binary string$$$^\dagger$$$ $$$s$$$ of length $$$n$$$.

A binary string $$$p$$$ of the same length $$$n$$$ is called good if for every $$$i$$$ ($$$1 \leq i \leq n$$$), there exist indices $$$l$$$ and $$$r$$$ such that:

$$$1 \leq l \leq i \leq r \leq n$$$
$$$s_i$$$ is a mode$$$^\ddagger$$$ of the string $$$p_lp_{l+1}\ldots p_r$$$

You are given another binary string $$$t$$$ of length $$$n$$$. Find the minimum Hamming distance$$$^\S$$$ between $$$t$$$ and any good string $$$g$$$.

$$$^\dagger$$$ A binary string is a string that only consists of characters $$$\mathtt{0}$$$ and $$$\mathtt{1}$$$.

$$$^\ddagger$$$ Character $$$c$$$ is a mode of string $$$p$$$ of length $$$m$$$ if the number of occurrences of $$$c$$$ in $$$p$$$ is at least $$$\lceil \frac{m}{2} \rceil$$$. For example, $$$\mathtt{0}$$$ is a mode of $$$\mathtt{010}$$$, $$$\mathtt{1}$$$ is not a mode of $$$\mathtt{010}$$$, and both $$$\mathtt{0}$$$ and $$$\mathtt{1}$$$ are modes of $$$\mathtt{011010}$$$.

$$$^\S$$$ The Hamming distance of strings $$$a$$$ and $$$b$$$ of length $$$m$$$ is the number of indices $$$i$$$ such that $$$1 \leq i \leq m$$$ and $$$a_i \neq b_i$$$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^5$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 10^4$$$) — the length of the binary string $$$s$$$.

The second line of each test case contains a binary string $$$s$$$ of length $$$n$$$ consisting of characters 0 and 1.

The third line of each test case contains a binary string $$$t$$$ of length $$$n$$$ consisting of characters 0 and 1.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^6$$$, with the additional assurance that the sum of $$$n^2$$$ over all test cases does not exceed $$$10^8$$$

Output

For each test case, print the minimum Hamming distance between $$$t$$$ and any good string $$$g$$$.

Note

In the first test case, $$$g=\mathtt{000}$$$ is a good string which has Hamming distance $$$0$$$ from $$$t$$$.

In the second test case, $$$g=\mathtt{0011}$$$ is a good string which has Hamming distance $$$2$$$ from $$$t$$$. It can be proven that there are no good strings with Hamming distance less than $$$2$$$ from $$$t$$$.

In the third test case, $$$g=\mathtt{001100}$$$ is a good string which has Hamming distance $$$1$$$ from $$$t$$$.

Minimum Hamming Distance

Examples