{"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\"\u003eAfter trying hard for many years, Little Q has finally received an astronaut license. To celebrate the fact, he intends to buy himself a spaceship and make an interstellar travel.\u003cbr\u003eLittle Q knows the position of $n$ planets in space, labeled by $1$ to $n$. To his surprise, these planets are all coplanar. So to simplify, Little Q put these $n$ planets on a plane coordinate system, and calculated the coordinate of each planet $(x_i,y_i)$.\u003cbr\u003eLittle Q plans to start his journey at the $1$-th planet, and end at the $n$-th planet. When he is at the $i$-th planet, he can next fly to the $j$-th planet only if $x_i\u0026lt;x_j$, which will cost his spaceship $x_i\\times y_j-x_j\\times y_i$ units of energy. Note that this cost can be negative, it means the flight will supply his spaceship.\u003cbr\u003ePlease write a program to help Little Q find the best route with minimum total cost.\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line of the input contains an integer $T(1\\leq T\\leq10)$, denoting the number of test cases.\u003cbr\u003eIn each test case, there is an integer $n(2\\leq n\\leq 200000)$ in the first line, denoting the number of planets.\u003cbr\u003eFor the next $n$ lines, each line contains $2$ integers $x_i,y_i(0\\leq x_i,y_i\\leq 10^9)$, denoting the coordinate of the $i$-th planet. Note that different planets may have the same coordinate because they are too close to each other. It is guaranteed that $y_1\u003dy_n\u003d0,0\u003dx_1\u0026lt;x_2,x_3,...,x_{n-1}\u0026lt;x_n$.\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print a single line containing several distinct integers $p_1,p_2,...,p_m(1\\leq p_i\\leq n)$, denoting the route you chosen is $p_1\\rightarrow p_2\\rightarrow...\\rightarrow p_{m-1}\\rightarrow p_m$. Obviously $p_1$ should be $1$ and $p_m$ should be $n$. You should choose the route with minimum total cost. If there are multiple best routes, please choose the one with the smallest lexicographically.\u003cbr\u003eA sequence of integers $a$ is lexicographically smaller than a sequence of $b$ if there exists such index $j$ that $a_i \u003d b_i$ for all $i \u0026lt; j$, but $a_j \u0026lt; b_j$.\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\n0 0\r\n3 0\r\n4 0\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1 2 3\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}