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

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <algorithm>
#include <iostream>
using namespace std;
int p,q,r,s,t;
bool sta[200];
char str[200];
int top;
void fun(char c)
{
    
    
 switch(c)
 {
    
    
  case 'K':
  {
    
    
   int x=sta[--top];
   int y=sta[--top];
   sta[top++]=(x&&y);
   break;
  }
  case 'A':
  {
    
    
   int x=sta[--top];
   int y=sta[--top];
   sta[top++]=(x||y);
   break;
  }
  case 'N':
  {
    
    
   int x=sta[--top];
   sta[top++]=!x;
   break;
  }
  case 'C':
  {
    
    
   int x=sta[--top];
   int y=sta[--top];
   sta[top++]=((!x)||y);
   break;
  }
  case 'E':
  {
    
    
   int x=sta[--top];
   int y=sta[--top];
   sta[top++]=(x==y);
   break;
  }
 }
}
void fun2(int i)
{
    
    
 switch(str[i])
 {
    
    
  case 'p':
  {
    
    
   if(p)
   sta[top++]=true;
   else
   sta[top++]=false;
   break;
  } 
  case 'q':
  {
    
    
   if(q)
   sta[top++]=true;
   else
   sta[top++]=false;
   break;
  } 
  case 'r':
  {
    
    
   if(r)
   sta[top++]=true;
   else
   sta[top++]=false;
   break;
  } 
  case 's':
  {
    
    
   if(s)
   sta[top++]=true;
   else
   sta[top++]=false;
   break;
  } 
  case 't':
  {
    
    
   if(t)
   sta[top++]=true;
   else
   sta[top++]=false;
   break;
  } 
 }
}
int main()
{
    
    
 while(cin>>str)
 {
    
    
  if(str[0]=='0') break;
  top=0;
  int len=strlen(str),flag=0;
  for(p=0;p<=1;p++)
  {
    
    
   for(q=0;q<=1;q++)
   {
    
    
    for(r=0;r<=1;r++)
    {
    
    
     for(s=0;s<=1;s++)
     {
    
    
      for(t=0;t<=1;t++)
      {
    
    
       for(int i=len-1;i>=0;i--)
       {
    
    
        if(str[i]=='p'||str[i]=='q'||str[i]=='r'||str[i]=='s'||str[i]=='t')
        {
    
    
         fun2(i);
        }
        else
        fun(str[i]);
       }
       if(!sta[--top])
       {
    
    
        flag=1;
        break;
       }
      }
      if(flag) break;
     }
     if(flag) break;
     } 
     if(flag) break;
   }
   if(flag) break;
  }
  if(!flag)
  printf("tautology\n");
  else
  printf("not\n");
 }
}