{"trustable":true,"prependHtml":"\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eProblems that require minimum paths through some domain appear in many different areas of computer science. For example, one of the constraints in VLSI routing problems is minimizing wire length. The Traveling Salesperson Problem (TSP) -- finding whether all the cities in a salesperson\u0027s route can be visited exactly once with a specified limit on travel time -- is one of the canonical examples of an NP-complete problem; solutions appear to require an inordinate amount of time to generate, but are simple to check. \u003cbr\u003e\u003cbr\u003eThis problem deals with finding a minimal path through a grid of points while traveling only from left to right. \u003cbr\u003e\u003cbr\u003eGiven an m*n matrix of integers, you are to write a program that computes a path of minimal weight. A path starts anywhere in column 1 (the first column) and consists of a sequence of steps terminating in column n (the last column). A step consists of traveling from column i to column i+1 in an adjacent (horizontal or diagonal) row. The first and last rows (rows 1 and m) of a matrix are considered adjacent, i.e., the matrix ``wraps\u0027\u0027 so that it represents a horizontal cylinder. Legal steps are illustrated below. \u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cimg style\u003d\"max-width:100%;\" src\u003d\"CDN_BASE_URL/022ee4c6101ca794ffd90f7070f5f140?v\u003d1714269936\"\u003e\u003cbr\u003e\u003cbr\u003eThe weight of a path is the sum of the integers in each of the n cells of the matrix that are visited. \u003cbr\u003e\u003cbr\u003eFor example, two slightly different 5*6 matrices are shown below (the only difference is the numbers in the bottom row). \u003cbr\u003e\u003cbr\u003e\u003cimg style\u003d\"max-width:100%;\" src\u003d\"CDN_BASE_URL/ef13810aed41e781fa4937f49c035392?v\u003d1714269936\"\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003eThe minimal path is illustrated for each matrix. Note that the path for the matrix on the right takes advantage of the adjacency property of the first and last rows. \u003cbr\u003e\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The input consists of a sequence of matrix specifications. Each matrix specification consists of the row and column dimensions in that order on a line followed by integers where m is the row dimension and n is the column dimension. The integers appear in the input in row major order, i.e., the first n integers constitute the first row of the matrix, the second n integers constitute the second row and so on. The integers on a line will be separated from other integers by one or more spaces. Note: integers are not restricted to being positive. There will be one or more matrix specifications in an input file. Input is terminated by end-of-file. \u003cbr\u003e\u003cbr\u003eFor each specification the number of rows will be between 1 and 10 inclusive; the number of columns will be between 1 and 100 inclusive. No path\u0027s weight will exceed integer values representable using 30 bits\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"Two lines should be output for each matrix specification in the input file, the first line represents a minimal-weight path, and the second line is the cost of a minimal path. The path consists of a sequence of n integers (separated by one or more spaces) representing the rows that constitute the minimal path. If there is more than one path of minimal weight the path that is lexicographically smallest should be output. \u003cbr\u003e\u003cbr\u003e"}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e5 6\r\n3 4 1 2 8 6\r\n6 1 8 2 7 4\r\n5 9 3 9 9 5\r\n8 4 1 3 2 6\r\n3 7 2 8 6 4\r\n5 6\r\n3 4 1 2 8 6\r\n6 1 8 2 7 4\r\n5 9 3 9 9 5\r\n8 4 1 3 2 6\r\n3 7 2 1 2 3\r\n2 2\r\n9 10 9 10\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1 2 3 4 4 5\r\n16\r\n1 2 1 5 4 5\r\n11\r\n1 1\r\n19\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}