Written by    16:03 July 22, 2014 


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


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 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.

Sample Input

Sample Output


这道题目我一开始读了半天还没读懂,后来请教了一位英文好的同学才弄懂了(还是学文的。。。),其实这道题就是离散数学里面的前缀表达式,输入由p、q、r、s、t、K、A、N、C、E共十个字母组成的逻辑表达式,其中p、q、r、s、t的值为1或者0,即逻辑变量; K、A、N、C、E为逻辑运算符, K-> and: x&&y A-> or: x||y N-> not: !x C-> implies: (!x)||y E-> equals: x==y 然后求在输入格式保证合法的前提下问逻辑表达式是否为永真式。





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