{"problem":{"name":"H and V","description":{"content":"We have a grid of $H$ rows and $W$ columns of squares. The color of the square at the $i$\\-th row from the top and the $j$\\-th column from the left $(1 \\leq i \\leq H, 1 \\leq j \\leq W)$ is given to you","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":1000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc173_c"},"statements":[{"statement_type":"Markdown","content":"We have a grid of $H$ rows and $W$ columns of squares. The color of the square at the $i$\\-th row from the top and the $j$\\-th column from the left $(1 \\leq i \\leq H, 1 \\leq j \\leq W)$ is given to you as a character $c_{i,j}$: the square is white if $c_{i,j}$ is `.`, and black if $c_{i,j}$ is `#`.\nConsider doing the following operation:\n\n*   Choose some number of rows (possibly zero), and some number of columns (possibly zero). Then, paint red all squares in the chosen rows and all squares in the chosen columns.\n\nYou are given a positive integer $K$. How many choices of rows and columns result in exactly $K$ black squares remaining after the operation? Here, we consider two choices different when there is a row or column chosen in only one of those choices.\n\n## Constraints\n\n*   $1 \\leq H, W \\leq 6$\n*   $1 \\leq K \\leq HW$\n*   $c_{i,j}$ is `.` or `#`.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$H$ $W$ $K$\n$c_{1,1}c_{1,2}...c_{1,W}$\n$c_{2,1}c_{2,2}...c_{2,W}$\n$:$\n$c_{H,1}c_{H,2}...c_{H,W}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc173_c","tags":[],"sample_group":[["2 3 2\n..#\n###","5\n\nFive choices below satisfy the condition.\n\n*   The $1$\\-st row and $1$\\-st column\n*   The $1$\\-st row and $2$\\-nd column\n*   The $1$\\-st row and $3$\\-rd column\n*   The $1$\\-st and $2$\\-nd column\n*   The $3$\\-rd column"],["2 3 4\n..#\n###","1\n\nOne choice, which is choosing nothing, satisfies the condition."],["2 2 3\n##\n##","0"],["6 6 8\n..##..\n.#..#.\n#....#\n######\n#....#\n#....#","208"]],"created_at":"2026-03-03 11:01:14"}}