Where to Build the Roads

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### Read problem statements in [Hindi](http://www.codechef.com/download/translated/MAY19/hindi/WTBTR.pdf), [Bengali](http://www.codechef.com/download/translated/MAY19/bengali/WTBTR.pdf), [Mandarin Chinese](http://www.codechef.com/download/translated/MAY19/mandarin/WTBTR.pdf), [Russian](http://www.codechef.com/download/translated/MAY19/russian/WTBTR.pdf), and [Vietnamese](http://www.codechef.com/download/translated/MAY19/vietnamese/WTBTR.pdf) as well. Chef bought a huge (effectively infinite) planar island and built $N$ restaurants (numbered $1$ through $N$) on it. For each valid $i$, the Cartesian coordinates of restaurant $i$ are $(X_i, Y_i)$. Now, Chef wants to build $N1$ straight narrow roads (line segments) on the island. The roads may have arbitrary lengths; restaurants do not have to lie on the roads. The slope of each road must be $1$ or $1$, i.e. for any two points $(x_1, y_1)$ and $(x_2, y_2)$ on the same road, $x_1x_2 = y_1y_2$ must hold. Let's denote the minimum distance Chef has to walk from restaurant $i$ to reach a road by $D_i$. Then, let's denote $a = \mathrm{max}\,(D_1, D_2, \ldots, D_N)$; Chef wants this distance to be minimum possible. Chef is a busy person, so he decided to give you the job of building the roads. You should find a way to build them that minimises $a$ and compute $a \cdot \sqrt{2}$. ### Input  The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.  The first line of each test case contains a single integer $N$.  $N$ lines follow. For each valid $i$, the $i$th of these lines contains two spaceseparated integers $X_i$ and $Y_i$. ### Output For each test case, print a single line containing one real number — the minimum distance $a$ multiplied by $\sqrt{2}$. Your answer will be considered correct if its absolute or relative error does not exceed $10^{6}$. ### Constraints  $1 \le T \le 100$  $2 \le N \le 10^4$  $X_i, Y_i \le 10^9$ for each valid $i$ ### Subtasks **Subtask #1 (10 points):**  $1 \le T \le 10$  $2 \le N \le 5$  $X_i, Y_i \le 10$ for each valid $i$  $a \cdot \sqrt{2}$ is an integer **Subtask #2 (90 points):** original constraints ### Example Input ``` 2 3 0 0 0 1 0 1 3 0 1 1 0 1 0 ``` ### Example Output ``` 0.5 0 ``` ### Explanation **Example case 1:** We should build roads described by equations $yx+0.5 = 0$ and $yx0.5 = 0$. **Example case 2:** We should build roads described by equations $yx1 = 0$ and $y+x1 = 0$.Author:  deepanshuvaid7 
Tags  deepanshuvaid7 
Date Added:  25042019 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, R, COB, FS 
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