시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

3차 논리는 논리값이 "true", "false", "unknown"을 가지는 논리 체계이다. 이 체계에서는 "false"는 0의 값을 가지고, "unknown"은 1, "true"는 2의 값을 갖는다.

"-"을 단항 연산자, "*"와 "+"는 이항 연산자라고 하자. 이 연산자는 각각 NOT, AND, OR을 의미한다. 3차 논리에서 3개 연산자는 다음과 같이 정의되어 있다.

P, Q, R을 3차 논리값을 갖는 변수라고 하자. 이 때, 식이 주어졌을 때, 식의 값을 2로 만드는 (P,Q,R)쌍의 개수를 구하는 프로그램을 작성하시오. 식은 다음 중 하나의 형태를 갖는다. (X와 Y는 식을 의미한다)

  • 상수: 0, 1, 2
  • 변수: P, Q, R
  • NOT: -X
  • AND: (X*Y)
  • OR: (X+Y)

AND와 OR은 항상 괄호로 둘러쌓여 있다.

예를 들어, (P*Q)가 주어졌을 때, 식의 값을 2로 만드는 (P,Q,R)쌍은 (2,2,0), (2,2,1), (2,2,2) 3가지이다.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스는 한 줄로 이루어져 있고, 식을 나타낸다. 식은 0, 1, 2, P, Q, R, -, *, +, (, )로만 이루어져 있다.

식의 BNF형 문법은 다음과 같다.

<formula> ::= 0 | 1 | 2 | P | Q | R |
              -<formula> | (<formula>*<formula>) | (<formula>+<formula>)

        

입력은 80글자를 넘지 않는다. 마지막 줄에는 '.'이 주어진다.

출력

각 테스트 케이스에 대해서, 입력으로 주어진 식의 값을 2로 만드는 (P,Q,R) 쌍의 개수를 출력한다.

예제 입력 1

(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.

예제 출력 1

3
11
0
27
0
7

힌트

[{"problem_id":"4970","problem_lang":"0","title":"\ub514\uc9c0\ud138 \ud68c\ub85c \uac1c\ub860","description":"<p>3\ucc28 \ub17c\ub9ac\ub294 \ub17c\ub9ac\uac12\uc774 &quot;true&quot;, &quot;false&quot;, &quot;unknown&quot;\uc744 \uac00\uc9c0\ub294 \ub17c\ub9ac \uccb4\uacc4\uc774\ub2e4. \uc774 \uccb4\uacc4\uc5d0\uc11c\ub294 &quot;false&quot;\ub294 0\uc758 \uac12\uc744 \uac00\uc9c0\uace0, &quot;unknown&quot;\uc740 1, &quot;true&quot;\ub294 2\uc758 \uac12\uc744 \uac16\ub294\ub2e4.<\/p>\r\n\r\n\r\n\r\n<p>&quot;-&quot;\uc744 \ub2e8\ud56d \uc5f0\uc0b0\uc790, &quot;*&quot;\uc640 &quot;+&quot;\ub294 \uc774\ud56d \uc5f0\uc0b0\uc790\ub77c\uace0 \ud558\uc790. \uc774 \uc5f0\uc0b0\uc790\ub294 \uac01\uac01 NOT, AND, OR\uc744 \uc758\ubbf8\ud55c\ub2e4. 3\ucc28 \ub17c\ub9ac\uc5d0\uc11c 3\uac1c \uc5f0\uc0b0\uc790\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub418\uc5b4 \uc788\ub2e4.<\/p>\r\n\r\n\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/tv.png\" style=\"height:187px; width:446px\" \/><\/p>\r\n\r\n\r\n\r\n<p>P, Q, R\uc744 3\ucc28 \ub17c\ub9ac\uac12\uc744 \uac16\ub294 \ubcc0\uc218\ub77c\uace0 \ud558\uc790. \uc774 \ub54c, \uc2dd\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc2dd\uc758 \uac12\uc744 2\ub85c \ub9cc\ub4dc\ub294 (P,Q,R)\uc30d\uc758 \uac1c\uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \uc2dd\uc740 \ub2e4\uc74c \uc911 \ud558\ub098\uc758 \ud615\ud0dc\ub97c \uac16\ub294\ub2e4. (X\uc640 Y\ub294 \uc2dd\uc744 \uc758\ubbf8\ud55c\ub2e4)<\/p>\r\n\r\n\r\n\r\n<ul>\r\n<li>\uc0c1\uc218: 0, 1, 2<\/li>\r\n\r\n<li>\ubcc0\uc218: P, Q, R<\/li>\r\n\r\n<li>NOT: -X<\/li>\r\n\r\n<li>AND: (X*Y)<\/li>\r\n\r\n<li>OR: (X+Y)<\/li><\/ul>\r\n\r\n\r\n<p>AND\uc640 OR\uc740 \ud56d\uc0c1 \uad04\ud638\ub85c \ub458\ub7ec\uc313\uc5ec \uc788\ub2e4.<\/p>\r\n\r\n\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, (P*Q)\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc2dd\uc758 \uac12\uc744 2\ub85c \ub9cc\ub4dc\ub294 (P,Q,R)\uc30d\uc740 (2,2,0), (2,2,1), (2,2,2) 3\uac00\uc9c0\uc774\ub2e4.<\/p>","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ud55c \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, \uc2dd\uc744 \ub098\ud0c0\ub0b8\ub2e4. \uc2dd\uc740 0, 1, 2, P, Q, R, -, *, +, (, )\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n\r\n\r\n<p>\uc2dd\uc758 BNF\ud615 \ubb38\ubc95\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n\r\n\r\n<pre>\r\n&lt;formula&gt; ::= 0 | 1 | 2 | P | Q | R |\r\n              -&lt;formula&gt; | (&lt;formula&gt;*&lt;formula&gt;) | (&lt;formula&gt;+&lt;formula&gt;)<\/pre>\r\n\r\n<p> &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<\/p>\r\n\r\n<p>\uc785\ub825\uc740 80\uae00\uc790\ub97c \ub118\uc9c0 \uc54a\ub294\ub2e4. \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 &#39;.&#39;\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \uc2dd\uc758 \uac12\uc744 2\ub85c \ub9cc\ub4dc\ub294 (P,Q,R) \uc30d\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"4970","problem_lang":"1","title":"How can I satisfy thee? Let me count the ways...","description":"<p>Three-valued logic is a logic system that has, in addition to &quot;true&quot; and &quot;false&quot;, &quot;unknown&quot; as a valid value. In the following, logical values &quot;false&quot;, &quot;unknown&quot; and &quot;true&quot; are represented by 0, 1 and 2 respectively.<\/p>\r\n\r\n<p>Let &quot;-&quot; be a unary operator (i.e. a symbol representing one argument function) and let both &quot;*&quot; and &quot;+&quot; be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.<\/p>\r\n\r\n<p>Table C-1: Truth tables of three-valued logic operators&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/tv.png\" style=\"height:187px; width:446px\" \/><\/p>\r\n\r\n<p>Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).<\/p>\r\n\r\n<ul>\r\n\t<li>Constants: 0, 1 or 2<\/li>\r\n\t<li>Variables: P, Q or R<\/li>\r\n\t<li>Negations: -X<\/li>\r\n\t<li>Conjunctions: (X*Y)<\/li>\r\n\t<li>Disjunctions: (X+Y)<\/li>\r\n<\/ul>\r\n\r\n<p>Note that conjunctions and disjunctions of two formulas are always parenthesized.<\/p>\r\n\r\n<p>For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.<\/p>\r\n","input":"<p>The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.<\/p>\r\n\r\n<pre>\r\n&lt;formula&gt; ::= 0 | 1 | 2 | P | Q | R |\r\n              -&lt;formula&gt; | (&lt;formula&gt;*&lt;formula&gt;) | (&lt;formula&gt;+&lt;formula&gt;)<\/pre>\r\n\r\n<p>All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.<\/p>\r\n\r\n<p>Finally, a line which contains only a &quot;.&quot; (period) comes, indicating the end of the input<\/p>\r\n","output":"<p>You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]