Time Limit: 1 s
Memory Limit: 128 MB

Submission：3
AC：3
Score：99.81

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, N*w*is a WFF - if
*w*and*x*are WFFs, K*wx*, A*wx*, C*wx*, and E*wx*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 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. For each test case, output a line containing *tautology* or *not* as appropriate.

Please Input Input Here

Please Input Output Here

input

ApNp
ApNq
0

output

tautology
not