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[102];
int f()
{
    int len=strlen(str);
    for(int i=len-1; i>-1; 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(0);
            else sta.push(1);
        }
        else if(str[i]=='E')
        {
            a=sta.top();
            sta.pop();
            b=sta.top();
            sta.pop();
            if(a==b)sta.push(1);
            else sta.push(0);
        }
        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=0; p<2; p++)
        for(q=0; q<2; q++)
            for(r=0; r<2; r++)
                for(s=0; s<2; s++)
                    for(t=0; t<2; t++)
                        if(!f())
                            return 0;
    return 1;
}
int main()
{
    while(gets(str))
    {
        if(!strcmp(str,"0"))
            break;
        else
        {
            if(sf())
                printf("tautology
");
            else
                printf("not
");
        }
    }
    return 0;
}