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code_segments/segment_189.txt

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+There is a grid, consisting of $2$ rows and $n$ columns. Each cell of the grid is either free or blocked.
+
+A free cell $y$ is reachable from a free cell $x$ if at least one of these conditions holds:
+
+  * $x$ and $y$ share a side;    * there exists a free cell $z$ such that $z$ is reachable from $x$ and $y$ is reachable from $z$. 
+
+A connected region is a set of free cells of the grid such that all cells in it are reachable from one another, but adding any other free cell to the set violates this rule.
+
+For example, consider the following layout, where white cells are free, and dark grey cells are blocked:
+
+![](CDN_BASE_URL/35b42e4e3c64eee3071df3d7b48861e8)
+
+There are $3$ regions in it, denoted with red, green and blue color respectively:
+
+![](CDN_BASE_URL/b2528153b76de41b1afcd49c1578a191)
+
+The given grid contains at most $1$ connected region. Your task is to calculate the number of free cells meeting the following constraint:
+
+  * if this cell is blocked, the number of connected regions becomes exactly $3$.
+
+The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.
+
+The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of columns.
+
+The $i$-th of the next two lines contains a description of the $i$-th row of the grid — the string $s_i$, consisting of $n$ characters. Each character is either . (denoting a free cell) or x (denoting a blocked cell).
+
+Additional constraint on the input:
+
+  * the given grid contains at most $1$ connected region;    * the sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$.
+
+For each test case, print a single integer — the number of cells such that the number of connected regions becomes $3$ if this cell is blocked.
+
+In the first test case, if the cell $(1, 3)$ is blocked, the number of connected regions becomes $3$ (as shown in the picture from the statement).