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

 #include<stdio.h>
 #include<iostream>
 #include<string.h>
 #include<stack>
 using namespace std;
 stack<int>sta;
 int p,q,r,s,t,a,b;
 char str[];
 int f()
 {
     int len=strlen(str);
     for(int i=len-; i>-; i--)
     {
         if(str[i]=='p')sta.push(p);//是字符直接入栈
         else if(str[i]=='q')sta.push(q);
         else if(str[i]=='r')sta.push(r);
         else if(str[i]=='s')sta.push(s);
         else if(str[i]=='t')sta.push(t);
         else if(str[i]=='K')//是运算就进行运算
         {
             a=sta.top();
             sta.pop();
             b=sta.top();
             sta.pop();
             sta.push(a&&b);
         }
         else if(str[i]=='A')
         {
             a=sta.top();
             sta.pop();
             b=sta.top();
             sta.pop();
             sta.push(a||b);
         }
         else if(str[i]=='C')
         {
             a=sta.top();
             sta.pop();
             b=sta.top();
             sta.pop();
             if(a&&!b)sta.push();
             else sta.push();
         }
         else if(str[i]=='E')
         {
             a=sta.top();
             sta.pop();
             b=sta.top();
             sta.pop();
             if(a==b)sta.push();
             else sta.push();
         }
         else if(str[i]=='N')
         {
             a=sta.top();
             sta.pop();
             sta.push(!a);
         }
     }
     return sta.top();
 }
 int sf()//枚举各种情况
 {
     for(p=; p<; p++)
         for(q=; q<; q++)
             for(r=; r<; r++)
                 for(s=; s<; s++)
                     for(t=; t<; t++)
                         if(!f())
                             return ;
     return ;
 }
 int main()
 {
     while(gets(str))
     {
         if(!strcmp(str,""))
             break;
         else
         {
             if(sf())
                 printf("tautology\n");
             else
                 printf("not\n");
         }
     }
     return ;
 }