{"trustable":true,"prependHtml":"\u003cstyle type\u003d\"text/css\"\u003e\n section pre {\n display: block;\n padding: 9.5px;\n margin: 0 0 10px;\n font-size: 13px;\n line-height: 1.42857143;\n word-break: break-all;\n word-wrap: break-word;\n color: #333;\n background: rgba(255, 255, 255, 0.5);\n border: 1px solid #ccc;\n border-radius: 6px;\n }\n\u003c/style\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\(\u0027, right: \u0027\\\\)\u0027, display: false},\n {left: \u0027\\\\[\u0027, right: \u0027\\\\]\u0027, display: true}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"Problem Statement","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eOn the \u003cvar\u003e\\(xy\\)\u003c/var\u003e-plane, we have a passage surrounded by the two lines \u003cvar\u003e\\(y\u003d-100\\)\u003c/var\u003e and \u003cvar\u003e\\(y\u003d100\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003cp\u003eIn the part of this passage with \u003cvar\u003e\\(-100 \u0026lt; x \u0026lt; 100\\)\u003c/var\u003e, there are \u003cvar\u003e\\(N\\)\u003c/var\u003e negligibly small nails. The coordinates of the \u003cvar\u003e\\(i\\)\u003c/var\u003e-th nail are \u003cvar\u003e\\((x_i, y_i)\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003cp\u003eTakahashi will choose a real number \u003cvar\u003e\\(r \\ (0 \u0026lt; r \\leq 100)\\)\u003c/var\u003e and put a circle of radius \u003cvar\u003e\\(r\\)\u003c/var\u003e so that its center is at \u003cvar\u003e\\((-10^9, 0)\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003cp\u003eThen, he will move the circle from \u003cvar\u003e\\((-10^9, 0)\\)\u003c/var\u003e to \u003cvar\u003e\\((10^9, 0)\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003cp\u003eHere, he continuously moves the circle so that the boundaries of the passage or the nails do not penetrate the interior of the circle.\u003c/p\u003e\r\n\u003cp\u003eFind the maximum possible value of \u003cvar\u003e\\(r\\)\u003c/var\u003e such that it is possible to move the circle to \u003cvar\u003e\\((10^9, 0)\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Constraints","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eAll values in input are integers.\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 \\leq N \\leq 100\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(|x_i|, |y_i| \u0026lt; 100\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003eIf \u003cvar\u003e\\(i \\neq j\\)\u003c/var\u003e, \u003cvar\u003e\\((x_i, y_i) \\neq (x_j, y_j)\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Input","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eInput is given from Standard Input in the following format:\u003c/p\u003e\r\n\u003cpre\u003e\u003cvar\u003e\\(N\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(x_1\\)\u003c/var\u003e \u003cvar\u003e\\(y_1\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(\\vdots\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(x_N\\)\u003c/var\u003e \u003cvar\u003e\\(y_N\\)\u003c/var\u003e\r\n\u003c/pre\u003e\r\n\r\n\u003c/section\u003e\r\n"}},{"title":"Output","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003ePrint the maximum possible value of \u003cvar\u003e\\(r\\)\u003c/var\u003e such that it is possible to move the circle to \u003cvar\u003e\\((10^9, 0)\\)\u003c/var\u003e.\r\nYour output will be considered correct when its absolute or relative error from our answer is at most \u003cvar\u003e\\(10^{-4}\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 1","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\u003e2\r\n0 -40\r\n0 40\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e40\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003cp\u003e\u003cimg alt\u003d\"\" src\u003d\"CDN_BASE_URL/c50e6c08b5992b834053708af0313f82?v\u003d1714060242\"\u003e\u003c/p\u003e\r\n\u003cp\u003eAs shown in the figure, we can move the circle with \u003cvar\u003e\\(r\u003d40\\)\u003c/var\u003e from \u003cvar\u003e\\((-10^9, 0)\\)\u003c/var\u003e to \u003cvar\u003e\\((10^9, 0)\\)\u003c/var\u003e by moving it along \u003cvar\u003e\\(y\u003d0\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003cp\u003eWhen \u003cvar\u003e\\(x\u003d0\\)\u003c/var\u003e, the circle exactly touches the two nails, which is fine since they do not penetrate the interior of the circle.\u003c/p\u003e\r\n\u003cp\u003eAny value of \u003cvar\u003e\\(r\\)\u003c/var\u003e greater than \u003cvar\u003e\\(40\\)\u003c/var\u003e makes it impossible to move the circle to \u003cvar\u003e\\((10^9, 0)\\)\u003c/var\u003e, so the maximum possible value is \u003cvar\u003e\\(r\u003d40\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 2","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\u003e4\r\n0 -10\r\n99 10\r\n0 91\r\n99 -91\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e50.5\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 3","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\u003e10\r\n-90 40\r\n20 -30\r\n0 -90\r\n10 -70\r\n80 70\r\n-90 30\r\n-20 -80\r\n10 90\r\n50 30\r\n60 -70\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e33.541019662496845446\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 4","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\u003e10\r\n65 -90\r\n-34 -2\r\n62 99\r\n42 -13\r\n47 -84\r\n84 87\r\n16 -78\r\n56 35\r\n90 8\r\n90 19\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e35.003571246374276203\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\u003c/section\u003e\r\n"}}]}