{"raw_statement":[{"iden":"statement","content":"You are given an $n \\times m$ grid. Some of the cells are obstacles, the others are empty. Choose a non-negative integer $k$ and color all empty cells with $k+1$ colors $0, 1, 2, \\ldots k$. You can not color two cells in the same row or same column with the same **non-zero** color. \n\nYou are given two non-negative integers $c$ and $d$. For a coloring plan, define $z$ as the number of the cells with color $0$. Define the cost of the plan is $ck+dz$.\n\nFind the minimum cost."},{"iden":"input","content":"The first line contains four integers $n$, $m$ ($1\\leq n, m\\leq 250$), $c$ and $d$ ($0\\leq c, d\\leq 10 ^ 9$).\n\nThe $i$-th line of the next $n$ lines contains a string of $m$ characters. The $j$-th character is `*` if the cell in the $i$-th row and the $j$-th column is an obstacle. The $j$-th character is `.` if the cell in the $i$-th row and the $j$-th column is empty."},{"iden":"output","content":"Output a line with a single number, representing the answer."},{"iden":"note","content":"**Source**: The 2022 ICPC Asia Xi'an Regional Contest Problem B.\n\n**Author**: csy2005."}],"translated_statement":null,"sample_group":[["3 4 2 1\n.***\n*..*\n**..\n","4\n"],["3 4 1 2\n.***\n*..*\n**..\n","2"]],"show_order":[],"formal_statement":null,"simple_statement":null,"has_page_source":false}