1414. Diceline

A die is a cube whose six faces are marked with 1, 2, 3, 4, 5 and 6 spots, respectively. The sum of the number of spots on opposite faces of a die is 7; that is, 1 and 6 appear on opposite faces, 2 and 5 appear on opposite faces, and 3 and 4 appear on opposite faces. This implies that it's possible to simultaneously see faces numbered 1, 2 and 3 by looking at one of corners; some dice arrange the faces numbered 1, 2, and 3 clockwise about their common corner, others arrange them counterclockwise about their common corner. Both clockwise and counterclockwise arrangements may occur here. In this problem, there are dicelines – collections of dice placed on a table and aligned from left to right by packing them as tightly as possible in a straight line. Each die has a face pointing north (N), a face pointing east (E), a face pointing south (S), a face pointing west (W), a face pointing up (U), and a face pointing down (D).

Input Format

The input contains one or more dicelines, each described by some successive nonempty lines followed by an empty line. The first line of a diceline contains a positive integer n giving the number of dice in the diceline. The individual dice in a diceline are referred to as die 0, die 1, die 2, …, die `n-1`. Each of the remaining input lines of a diceline reveal some information about numbers facing a direction; specifically, each line contains a direction `d\ ∈\ `{N, E, S, W, U, D}, a colon (:), and `n` numbers `∈` {0, 1, 2, 3, 4, 5, 6} separated by commas (,) describing the numbers on die 0, die 1, die 2, …, die `n-1` facing direction `d`. If the number 0 is given for a face of die `i`, then no information is given about the number on that face.

Output Format

For each diceline in the input, the numbers given for faces of die i either give too little information to determine the numbers facing each direction (i.e. unknown), give enough information to uniquely determine the numbers facing each direction (i.e. known), or give inconsistent information that is physically impossible to realize on a clockwise or counterclockwise die (i.e. inconsistent). For each die in the diceline, report whether the die is unknown, known, or inconsistent as shown in the output sample.

1
U:1
S:2
W:3

10
N:3,4,5,0,1,0,0,1,1,6
E:0,2,0,0,5,2,1,4,2,0
U:1,6,2,0,0,4,0,5,3,5
W:0,5,0,0,3,5,6,0,0,4

die 0 is known

die 0 is unknown
die 1 is known
die 2 is inconsistent
die 3 is unknown
die 4 is inconsistent
die 5 is unknown
die 6 is unknown
die 7 is known
die 8 is known
die 9 is known