Tautology

Description

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

//类似于后缀式求值；

#include<stdio.h>
#include<string.h>
#include<stack>
using namespace std;

char ss[101];
stack <int> st;
int flag;

void check(int p, int q, int r, int s,int t)
{
    while(!st.empty())
        st.pop();
    int a,b;
    int len = strlen(ss);
    for(int i = len-1; i >= 0; i--)
    {
        if(ss[i] == 'p')
            st.push(p);
        else if(ss[i] == 'q')
            st.push(q);
        else if(ss[i] == 'r')
            st.push(r);
        else if(ss[i] == 's')
            st.push(s);
        else if(ss[i] == 't')
            st.push(t);
        else if(ss[i] == 'K')
        {
            a = st.top();
            st.pop();
            b = st.top();
            st.pop();
            if(a == 1 && b == 1)
                st.push(1);
            else st.push(0);
        }
        else if(ss[i] == 'A')
        {
            a = st.top();
            st.pop();
            b = st.top();
            st.pop();
            if(a == 0 && b == 0)
                st.push(0);
            else st.push(1);
        }
        else if(ss[i] == 'N')
        {
            a = st.top();
            st.pop();
            if(a == 1)
                st.push(0);
            else st.push(1);
        }
        else if(ss[i] == 'C')
        {
            a = st.top();
            st.pop();
            b = st.top();
            st.pop();
            if(a == 0 && b == 1)
                st.push(0);
            else st.push(1);
        }
        else if(ss[i] == 'E')
        {
            a = st.top();
            st.pop();
            b = st.top();
            st.pop();
            st.push((a && b) || (!a && !b));
        }
    }
    if(st.top() != 1)
        flag = 0;
}
int main()
{
    while(~scanf("%s",ss))
    {
        flag = 1;
        if(strcmp("0",ss) == 0)
            break;
        for(int p = 0; p < 2; p++)
            for(int q = 0; q < 2; q++)
                for(int r = 0; r < 2; r++)
                    for(int s = 0; s < 2; s++)
                        for(int t = 0; t < 2; t++)
                            check(p, q, r, s, t);
        if(flag == 1)
            printf("tautology
");
        else printf("not
");
    }
    return 0;
}