{"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\"\u003eThere are $n$ cities in Byteland, labeled by $1$ to $n$. The $i$-th city is located at $(x_i,y_i)$.\u003cbr\u003eThe Transport Construction Authority of Byteland is planning to open several bidirectional flights. Opening flight between the $i$-th city and the $j$-th city will cost $x_i\\times x_j+y_i\\times y_j$ dollars.\u003cbr\u003eThe Transport Construction Authority is now searching for the cheapest way to connect all of $n$ cities, so that every pair of different cities are connected by these flights directly or indirectly. Please write a program to find the cheapest way.\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line of the input contains an integer $T(1\\leq T\\leq2000)$, denoting the number of test cases.\u003cbr\u003eIn each test case, there is an integer $n(2\\leq n\\leq 100000)$ in the first line, denoting the number of cities in Byteland.\u003cbr\u003eFor the next $n$ lines, each line contains $2$ integers $x_i,y_i(1\\leq x_i,y_i\\leq 10^6)$, denoting the coordinate of the $i$-th city. Note that different cities may have the same coordinate because they are too close to each other.\u003cbr\u003eIt is guaranteed that $\\sum n\\leq 10^6$.\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print a single line containing an integer, denoting the minimum total cost.\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\u003e1\r\n3\r\n2 4\r\n3 1\r\n5 2\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e27\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}