{"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\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027$$$$$$\u0027, right: \u0027$$$$$$\u0027, display: true},\n {left: \u0027$$$\u0027, right: \u0027$$$\u0027, display: false},\n {left: \u0027$$\u0027, right: \u0027$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eYou\u0027re given an integer $$$n$$$. For every integer $$$i$$$ from $$$2$$$ to $$$n$$$, assign a positive integer $$$a_i$$$ such that the following conditions hold:\u003c/p\u003e\u003cul\u003e \u003cli\u003e For any pair of integers $$$(i,j)$$$, if $$$i$$$ and $$$j$$$ are coprime, $$$a_i \\neq a_j$$$. \u003c/li\u003e\u003cli\u003e The maximal value of all $$$a_i$$$ should be minimized (that is, as small as possible). \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eA pair of integers is called \u003ca href\u003d\"https://en.wikipedia.org/wiki/Coprime_integers\"\u003ecoprime\u003c/a\u003e if their \u003ca href\u003d\"https://en.wikipedia.org/wiki/Greatest_common_divisor\"\u003egreatest common divisor\u003c/a\u003e is $$$1$$$.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe only line contains the integer $$$n$$$ ($$$2 \\le n \\le 10^5$$$).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint $$$n-1$$$ integers, $$$a_2$$$, $$$a_3$$$, $$$\\ldots$$$, $$$a_n$$$ ($$$1 \\leq a_i \\leq n$$$). \u003c/p\u003e\u003cp\u003eIf there are multiple solutions, print any of them.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1 2 1 \u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2 1\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eIn the first example, notice that $$$3$$$ and $$$4$$$ are coprime, so $$$a_3 \\neq a_4$$$. Also, notice that $$$a\u003d[1,2,3]$$$ satisfies the first condition, but it\u0027s not a correct answer because its maximal value is $$$3$$$.\u003c/p\u003e"}}]}