{"raw_statement":[{"iden":"problem statement","content":"There is a square-shaped grid with $N$ vertical rows and $N$ horizontal columns. We will denote the square at the $i$\\-th row from the top and the $j$\\-th column from the left as $(i,\\ j)$.\nInitially, each square is either white or black. The initial color of the grid is given to you as characters $a_{ij}$, arranged in a square shape. If the square $(i,\\ j)$ is white, $a_{ij}$ is `.`. If it is black, $a_{ij}$ is `#`.\nYou are developing a robot that repaints the grid. It can repeatedly perform the following operation:\n\n*   Select two integers $i$, $j$ ($1 ≤ i,\\ j ≤ N$). Memorize the colors of the squares $(i,\\ 1)$, $(i,\\ 2)$, $...$, $(i,\\ N)$ as $c_1$, $c_2$, $...$, $c_N$, respectively. Then, repaint the squares $(1,\\ j)$, $(2,\\ j)$, $...$, $(N,\\ j)$ with the colors $c_1$, $c_2$, $...$, $c_N$, respectively.\n\nYour objective is to turn all the squares black. Determine whether it is possible, and find the minimum necessary number of operations to achieve it if the answer is positive."},{"iden":"constraints","content":"*   $2 ≤ N ≤ 500$\n*   $a_{ij}$ is either `.` or `#`."},{"iden":"partial score","content":"*   In a test set worth $300$ points, $N ≤ 3$."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$a_{11}$$...$$a_{1N}$\n$:$\n$a_{N1}$$...$$a_{NN}$"},{"iden":"sample input 1","content":"2\n#.\n.#"},{"iden":"sample output 1","content":"3\n\nFor example, perform the operation as follows:\n\n*   Select $i = 1$, $j = 2$.\n*   Select $i = 1$, $j = 1$.\n*   Select $i = 1$, $j = 2$.\n\nThe transition of the colors of the squares is shown in the figure below:\n\n![image](https://atcoder.jp/img/mujin/6a0314bb2b1073694a7ef5a062e77b13.png)"},{"iden":"sample input 2","content":"2\n..\n.."},{"iden":"sample output 2","content":"\\-1"},{"iden":"sample input 3","content":"2\n##\n##"},{"iden":"sample output 3","content":"0"},{"iden":"sample input 4","content":"3\n.#.\n###\n.#."},{"iden":"sample output 4","content":"2"},{"iden":"sample input 5","content":"3\n...\n.#.\n..."},{"iden":"sample output 5","content":"5"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}