{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eMike\u0027s living room is covered by $$$m^2$$$ square tiles. These tiles form a $$$m \\times m$$$ grid in which rows are numbered with $$$1$$$ through $$$m$$$ from top to bottom and columns are numbered with $$$1$$$ through $$$m$$$ from left to right.\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/cb881be9033d55320af586e349017a65?v\u003d1715727754\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e\u003cp\u003eAbove these tiles on the floor are laying $$$n$$$ rectangular carpets whose sides are parallel to sides of the grid. Each carpet covers the intersection of several consecutive rows and several consecutive columns, forming a rectangle. Precisely speaking, the $$$i$$$-th carpet of them is described by four integers $$$x_l, x_r, y_l, y_r$$$ with $$$1 \\leq x_l \\leq x_r \\leq m$$$ and $$$1 \\leq y_l \\leq y_r \\leq m$$$, indicating that the carpet covers all tiles which are both ranged from the $$$x_l$$$-th row to the $$$x_r$$$-th row and ranged from the $$$y_l$$$-th column to the $$$y_r$$$-th column.\u003c/p\u003e\u003cp\u003eNow Mike asks you to take away \u003cspan class\u003d\"tex-font-style-bf\"\u003eexactly two\u003c/span\u003e carpets of them, in order to minimize the number of tiles that would still be covered by at least one remaining carpet.\u003c/p\u003e\u003cp\u003eThe figure provided above describes the sample case, in which those two rectangular regions with imaginary boundaries indicate an optimal removal of two carpets.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe input contains several test cases, and the first line contains a positive integer $$$T$$$ indicating the number of test cases which is up to $$$1000$$$.\u003c/p\u003e\u003cp\u003eFor each test case, the first line contains two integers $$$n$$$ and $$$m$$$ indicating the number of carpets and the number of tiles in each row or column, where $$$3 \\leq n \\leq 3 \\times 10^5$$$ and $$$1 \\leq m \\leq 1500$$$.\u003c/p\u003e\u003cp\u003eEach of the following $$$n$$$ lines contains four integers $$$x_l$$$, $$$x_r$$$, $$$y_l$$$, $$$y_r$$$ describing a carpet laying on the floor and its postion, where $$$1 \\leq x_l \\leq x_r \\leq m$$$ and $$$1 \\leq y_l \\leq y_r \\leq m$$$.\u003c/p\u003e\u003cp\u003eWe guarantee that the sum of $$$n$$$ in all test cases is up to $$$2 \\times 10^6$$$, while the sum of $$$m^2$$$ in all test cases is up to $$$5 \\times 10^7$$$.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each test case, output a line containing the minimum number of tiles that would still be covered by at least one remaining carpet after removal of two carpets.\u003c/p\u003e"}},{"title":"Examples","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\u003e1\n4 5\n1 1 3 3\n2 2 4 4\n3 3 5 5\n2 3 1 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}