{"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\u003eThere are infinitely many cards, numbered \u003cvar\u003e\\(1\\)\u003c/var\u003e, \u003cvar\u003e\\(2\\)\u003c/var\u003e, \u003cvar\u003e\\(3\\)\u003c/var\u003e, \u003cvar\u003e\\(...\\)\u003c/var\u003e\r\nInitially, Cards \u003cvar\u003e\\(x_1\\)\u003c/var\u003e, \u003cvar\u003e\\(x_2\\)\u003c/var\u003e, \u003cvar\u003e\\(...\\)\u003c/var\u003e, \u003cvar\u003e\\(x_N\\)\u003c/var\u003e are face up, and the others are face down.\u003c/p\u003e\r\n\u003cp\u003eSnuke can perform the following operation repeatedly:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eSelect a prime \u003cvar\u003e\\(p\\)\u003c/var\u003e greater than or equal to \u003cvar\u003e\\(3\\)\u003c/var\u003e. Then, select \u003cvar\u003e\\(p\\)\u003c/var\u003e consecutive cards and flip all of them.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eSnuke\u0027s objective is to have all the cards face down.\r\nFind the minimum number of operations required to achieve the objective.\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\u003e\u003cvar\u003e\\(1 ≤ N ≤ 100\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 ≤ x_1 \u0026lt; x_2 \u0026lt; ... \u0026lt; x_N ≤ 10^7\\)\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\\(x_2\\)\u003c/var\u003e \u003cvar\u003e\\(...\\)\u003c/var\u003e \u003cvar\u003e\\(x_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 minimum number of operations required to achieve the objective.\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\n4 5\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2\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\u003eBelow is one way to achieve the objective in two operations:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eSelect \u003cvar\u003e\\(p \u003d 5\\)\u003c/var\u003e and flip Cards \u003cvar\u003e\\(1\\)\u003c/var\u003e, \u003cvar\u003e\\(2\\)\u003c/var\u003e, \u003cvar\u003e\\(3\\)\u003c/var\u003e, \u003cvar\u003e\\(4\\)\u003c/var\u003e and \u003cvar\u003e\\(5\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003cli\u003eSelect \u003cvar\u003e\\(p \u003d 3\\)\u003c/var\u003e and flip Cards \u003cvar\u003e\\(1\\)\u003c/var\u003e, \u003cvar\u003e\\(2\\)\u003c/var\u003e and \u003cvar\u003e\\(3\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003c/ul\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\u003e9\r\n1 2 3 4 5 6 7 8 9\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\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\u003eBelow is one way to achieve the objective in three operations:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eSelect \u003cvar\u003e\\(p \u003d 3\\)\u003c/var\u003e and flip Cards \u003cvar\u003e\\(1\\)\u003c/var\u003e, \u003cvar\u003e\\(2\\)\u003c/var\u003e and \u003cvar\u003e\\(3\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003cli\u003eSelect \u003cvar\u003e\\(p \u003d 3\\)\u003c/var\u003e and flip Cards \u003cvar\u003e\\(4\\)\u003c/var\u003e, \u003cvar\u003e\\(5\\)\u003c/var\u003e and \u003cvar\u003e\\(6\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003cli\u003eSelect \u003cvar\u003e\\(p \u003d 3\\)\u003c/var\u003e and flip Cards \u003cvar\u003e\\(7\\)\u003c/var\u003e, \u003cvar\u003e\\(8\\)\u003c/var\u003e and \u003cvar\u003e\\(9\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003c/ul\u003e\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\u003e2\r\n1 10000000\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4\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"}}]}