HZNUOJ

WFF

Tags:
Time Limit:  1 s      Memory Limit:   128 MB Special Judge
Submission:1     AC:0     Score:99.98

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:

The meaning of a WFF is defined as follows:

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

Given a collection of symbols resulting from throwing a set of dice, determine the longest WFF that can be formed from those symbols.

Input consists of several test cases. Each test case is a single line containing a string containing between 1 and 100 of the characters. A line containing 0 follows the last case. For each test case, output a line containing the longest WFF that can be formed using some subset of the letters in the string. If there are several such WFFs, any one will do. If no WFF can be constructed, output a line containing "no WFF possible" as shown below.

Samples

input
qKpNq KKN 0
output
KqNq no WFF possible