{"trustable":true,"prependHtml":"\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\(\u0027, right: \u0027\\\\)\u0027, display: false},\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"MD","content":"### Problem\n\nGiven a two-dimensional array of positive and negative integers, a sub-rectangle is any contiguous sub-array of size 1 x 1 or greater located within the whole array. The sum of a rectangle is the sum of all the elements in that rectangle. In this problem the sub-rectangle with the largest sum is referred to as the maximal sub-rectangle.\n\nAs an example, the maximal sub-rectangle of the array:\n\n```plain\n0 -2 -7 0\n9 2 -6 2\n-4 1 -4 1\n-1 8 0 -2\n```\n\nis in the lower left corner:\n\n```plain\n9 2\n-4 1\n-1 8\n```\n\nand has a sum of 15.\n\n### Input\n\nThe input consists of an N x N array of integers. The input begins with a single positive integer N on a line by itself, indicating the size of the square two-dimensional array. This is followed by N 2 integers separated by whitespace (spaces and newlines). These are the N 2 integers of the array, presented in row-major order. That is, all numbers in the first row, left to right, then all numbers in the second row, left to right, etc. N may be as large as 100. The numbers in the array will be in the range [-127,127].\n\n### Output\n\nOutput the sum of the maximal sub-rectangle.\n\n### Example Input\n\n```in\n4\n0 -2 -7 0 9 2 -6 2\n-4 1 -4 1 -1\n8 0 -2\n```\n\n### Example Output\n\n```out\n15\n```\n"}}]}