{"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\u003eGiven are \u003cvar\u003e\\(N\\)\u003c/var\u003e strings \u003cvar\u003e\\(S_1,\\ldots,S_N\\)\u003c/var\u003e, each of which is \u003ccode\u003eAND\u003c/code\u003e or \u003ccode\u003eOR\u003c/code\u003e.\u003c/p\u003e\r\n\u003cp\u003eFind the number of tuples of \u003cvar\u003e\\(N+1\\)\u003c/var\u003e variables \u003cvar\u003e\\((x_0,\\ldots,x_N)\\)\u003c/var\u003e, where each element is \u003cvar\u003e\\(\\text{True}\\)\u003c/var\u003e or \u003cvar\u003e\\(\\text{False}\\)\u003c/var\u003e, such that the following computation results in \u003cvar\u003e\\(y_N\\)\u003c/var\u003e being \u003cvar\u003e\\(\\text{True}\\)\u003c/var\u003e:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(y_0\u003dx_0\\)\u003c/var\u003e;\u003c/li\u003e\r\n\u003cli\u003efor \u003cvar\u003e\\(i\\geq 1\\)\u003c/var\u003e, \u003cvar\u003e\\(y_i\u003dy_{i-1} \\land x_i\\)\u003c/var\u003e if \u003cvar\u003e\\(S_i\\)\u003c/var\u003e is \u003ccode\u003eAND\u003c/code\u003e, and \u003cvar\u003e\\(y_i\u003dy_{i-1} \\lor x_i\\)\u003c/var\u003e if \u003cvar\u003e\\(S_i\\)\u003c/var\u003e is \u003ccode\u003eOR\u003c/code\u003e.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eHere, \u003cvar\u003e\\(a \\land b\\)\u003c/var\u003e and \u003cvar\u003e\\(a \\lor b\\)\u003c/var\u003e are logical operators.\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 \\leq N \\leq 60\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(S_i\\)\u003c/var\u003e is \u003ccode\u003eAND\u003c/code\u003e or \u003ccode\u003eOR\u003c/code\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\\(S_1\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(\\vdots\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(S_N\\)\u003c/var\u003e\r\n\u003c/pre\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Output","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003ePrint the answer.\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\nAND\r\nOR\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e5\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\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\u003cp\u003eFor example, if \u003cvar\u003e\\((x_0,x_1,x_2)\u003d(\\text{True},\\text{False},\\text{True})\\)\u003c/var\u003e, we have \u003cvar\u003e\\(y_2 \u003d \\text{True}\\)\u003c/var\u003e, as follows:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(y_0\u003dx_0\u003d\\text{True}\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(y_1\u003dy_0 \\land x_1 \u003d \\text{True} \\land \\text{False}\u003d\\text{False}\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(y_2\u003dy_1 \\lor x_2 \u003d \\text{False} \\lor \\text{True}\u003d\\text{True}\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eAll of the five tuples \u003cvar\u003e\\((x_0,x_1,x_2)\\)\u003c/var\u003e resulting in \u003cvar\u003e\\(y_2 \u003d \\text{True}\\)\u003c/var\u003e are shown below:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003e\u003cvar\u003e\\((\\text{True},\\text{True},\\text{True})\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\((\\text{True},\\text{True},\\text{False})\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\((\\text{True},\\text{False},\\text{True})\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\((\\text{False},\\text{True},\\text{True})\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\((\\text{False},\\text{False},\\text{True})\\)\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\u003e5\r\nOR\r\nOR\r\nOR\r\nOR\r\nOR\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e63\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\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\u003cp\u003eAll tuples except the one filled entirely with \u003cvar\u003e\\(\\text{False}\\)\u003c/var\u003e result in \u003cvar\u003e\\(y_5 \u003d \\text{True}\\)\u003c/var\u003e.\u003c/p\u003e\u003c/section\u003e\r\n"}}]}