{"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":"\n\u003csection\u003e\n\u003cp\u003eThere are \u003cvar\u003e\\(N\\)\u003c/var\u003e piles of stones. Initially, the \u003cvar\u003e\\(i\\)\u003c/var\u003e-th pile contains \u003cvar\u003e\\(A_i\\)\u003c/var\u003e stones. With these piles, Taro the First and Jiro the Second play a game against each other.\u003c/p\u003e\n\u003cp\u003eTaro the First and Jiro the Second make the following move alternately, with Taro the First going first:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eChoose a pile of stones, and remove between \u003cvar\u003e\\(L\\)\u003c/var\u003e and \u003cvar\u003e\\(R\\)\u003c/var\u003e stones (inclusive) from it.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eA player who is unable to make a move loses, and the other player wins. Who wins if they optimally play to win?\u003c/p\u003e\n\u003c/section\u003e\n"}},{"title":"Constraints","value":{"format":"HTML","content":"\n\u003csection\u003e\n\u003cul\u003e\n\u003cli\u003e\u003cvar\u003e\\(1\\leq N \\leq 2\\times 10^5\\)\u003c/var\u003e\u003c/li\u003e\n\u003cli\u003e\u003cvar\u003e\\(1\\leq L \\leq R \\leq 10^9\\)\u003c/var\u003e\u003c/li\u003e\n\u003cli\u003e\u003cvar\u003e\\(1\\leq A_i \\leq 10^9\\)\u003c/var\u003e\u003c/li\u003e\n\u003cli\u003eAll values in the input are integers.\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/section\u003e\n"}},{"title":"Input","value":{"format":"HTML","content":"\n\u003csection\u003e\n\u003cp\u003eThe input is given from Standard Input in the following format:\u003c/p\u003e\n\u003cpre\u003e\u003cvar\u003e\\(N\\)\u003c/var\u003e \u003cvar\u003e\\(L\\)\u003c/var\u003e \u003cvar\u003e\\(R\\)\u003c/var\u003e \n\u003cvar\u003e\\(A_1\\)\u003c/var\u003e \u003cvar\u003e\\(A_2\\)\u003c/var\u003e \u003cvar\u003e\\(\\ldots\\)\u003c/var\u003e \u003cvar\u003e\\(A_N\\)\u003c/var\u003e\n\u003c/pre\u003e\n\u003c/section\u003e\n"}},{"title":"Output","value":{"format":"HTML","content":"\n\u003csection\u003e\n\u003cp\u003ePrint \u003ccode\u003eFirst\u003c/code\u003e if Taro the First wins; print \u003ccode\u003eSecond\u003c/code\u003e if Jiro the Second wins.\u003c/p\u003e\n\u003c/section\u003e\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\u003e3 1 2\n2 3 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eFirst\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\n\u003csection\u003e\n\n\u003c/section\u003e\n\n\u003csection\u003e\n\n\u003cp\u003eTaro the First can always win by removing two stones from the first pile in his first move.\u003c/p\u003e\n\u003c/section\u003e\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\u003e5 1 1\n3 1 4 1 5\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eSecond\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\n\u003csection\u003e\n\n\u003c/section\u003e\n\n\u003csection\u003e\n\n\u003c/section\u003e\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\u003e7 3 14\n10 20 30 40 50 60 70\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eFirst\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\n\u003csection\u003e\n\n\u003c/section\u003e\n\n\u003csection\u003e\n\u003c/section\u003e\n"}}]}