Tautology

WFF ‘N PROOF is a logic game played with dice. Each die has six faces representing some subset of the possible symbols K, A, N, C, E, p, q, r, s, t. A Well-formed formula WFF) is any string of these symbols obeying the following rules:

p, q, r, s, and t are WFFs
if w is a WFF, Nw is a WFF
if w and x are WFFs, Kwx, Awx, Cwx, and Ewx are WFFs.

The meaning of a WFF is defined as follows:

p, q, r, s, and t are logical variables that may take on the value 0 false) or 1 true).
K, A, N, C, E mean and, or, not, implies, and equals as defined in the truth table below.

Definitions of K, A, N, C, and E

w  x	Kwx	Awx	Nw	Cwx	Ewx
1  1	1	1	0	1	1
1  0	0	1	0	0	0
0  1	0	1	1	1	0
0  0	0	0	1	1	1

A tautology is a WFF that has value 1 true) regardless of the values of its variables. For example, ApNp is a tautology because it is true regardless of the value of p. On the other hand, ApNq is not, because it has the value 0 for p=0, q=1.

You must determine whether or not a WFF is a tautology.

Input

Input consists of several test cases. Each test case is a single line containing a WFF with no more than 100 symbols. A line containing 0 follows the last case.

Output

For each test case, output a line containing tautology or not as appropriate.

Sample Input

ApNp
ApNq
0

Sample Output

tautology
not

就是离散数学的一个模拟，判断所给的式子是不是永真公式
用栈逆序推还不算难

 1 #include<stdio.h>
 2 #include<iostream>
 3 #include<string.h>
 4 #include<stack>
 5 using namespace std;
 6 stack<int>sta;
 7 int p,q,r,s,t,a,b;
 8 char str[102];
 9 int f)
10 {
11     int len=strlenstr);
12     forint i=len-1; i>-1; i--)
13     {
14         ifstr[i]=='p')sta.pushp);//是字符直接入栈
15         else ifstr[i]=='q')sta.pushq);
16         else ifstr[i]=='r')sta.pushr);
17         else ifstr[i]=='s')sta.pushs);
18         else ifstr[i]=='t')sta.pusht);
19         else ifstr[i]=='K')//是运算就进行运算
20         {
21             a=sta.top);
22             sta.pop);
23             b=sta.top);
24             sta.pop);
25             sta.pusha&&b);
26         }
27         else ifstr[i]=='A')
28         {
29             a=sta.top);
30             sta.pop);
31             b=sta.top);
32             sta.pop);
33             sta.pusha||b);
34         }
35         else ifstr[i]=='C')
36         {
37             a=sta.top);
38             sta.pop);
39             b=sta.top);
40             sta.pop);
41             ifa&&!b)sta.push0);
42             else sta.push1);
43         }
44         else ifstr[i]=='E')
45         {
46             a=sta.top);
47             sta.pop);
48             b=sta.top);
49             sta.pop);
50             ifa==b)sta.push1);
51             else sta.push0);
52         }
53         else ifstr[i]=='N')
54         {
55             a=sta.top);
56             sta.pop);
57             sta.push!a);
58         }
59     }
60     return sta.top);
61 }
62 int sf)//枚举各种情况
63 {
64     forp=0; p<2; p++)
65         forq=0; q<2; q++)
66             forr=0; r<2; r++)
67                 fors=0; s<2; s++)
68                     fort=0; t<2; t++)
69                         if!f))
70                             return 0;
71     return 1;
72 }
73 int main)
74 {
75     whilegetsstr))
76     {
77         if!strcmpstr,"0"))
78             break;
79         else
80         {
81             ifsf))
82                 printf"tautology
");
83             else
84                 printf"not
");
85         }
86     }
87     return 0;
88 }

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