# POJ3295

Written by    16:03 July 22, 2014

POJ3295

Tautology
 Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 10897 Accepted: 4136

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, ApNqis 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

Sample Output

Source

Category : acmstudy

Tags :