The simplest problem about cubes

Time limit2sMemory limit1024 MB

Summary

Given the colors and numbers on three visible faces of a cube, list every collector whose criteria allow that cube.

Level: Easy2 of 10
Topics: Implementation
Solved: No attempts yet

Statement

Yesterday Taja visited the museum. The tour was long and interesting, but the room she liked most contained collections of the cubes of ten famous collectors. One of the cubes caught her attention, but she forgot which collector possessed it. Nevertheless she memorized how three visible faces looked, as well as the criteria of each collector. Deduce the names of the collectors who could possess such a cube from this information.

Each cube has $6$ faces. Each face has a single number written on it from $1$ to $6$ , unique for each face. Numbers can be represented either by dots, as a decimal, or as a Roman numeral. Each face also has one of the following colors: Black, White, Green, Yellow, Skyblue, Red, Orange and Purple.

Here is the list of the collectors and their criteria, which hold for the entire collection:


John	All numbers are represented as dots
David	Numbers are never written as Roman numerals
Peter	All faces are white
Robert	Faces of the cube are either black or white
Mark	Odd numbers have a white background, even numbers have a black background
Paul	All prime numbers are written as decimal, and all decimal numbers are prime
Patrick	All faces have the same color, but the color is neither black nor white
Jack	All Roman numerals are on a yellow background
Max	All faces have unique colors
Alex	Numbers of the same format have the same background, and different formats have different colors

Input

The input has three lines, describing the visible faces of the cube.

The first symbol of the $i$ th line $c_i$ ( $c_i \in \{B, W, G, Y, S, R, O, P\}$ ) is the color of the $i$ th face (Black, White, Green, Yellow, Skyblue, Red, Orange and Purple respectively). After a space follows the number written on the face, in one of these formats:

From $1$ to $6$ . symbols (ASCII $46$ ), where the number of dots equals the number on the face;
A decimal number from $1$ to $6$ ;
A Roman numeral written with I (ASCII $73$ ) and V (ASCII $86$ ) symbols.

It is guaranteed that the presented cube belongs to at least one collector.

Output

Print a single line with the names of the collectors who can own the given cube. The names can be in any order and are separated by spaces.

All names must come from this list: John, David, Peter, Robert, Mark, Paul, Patrick, Jack, Max, Alex.

Examples5

Example 1

Input

W ..
W ...
W ....

Expected output

John David Peter Robert Jack Alex

Example 2
Input
```
B 2
W 3
B 6
```
Expected output
```
David Robert Mark Jack 
```
Example 3
Input
```
G 1
G 2
G V
```
Expected output
```
Patrick
```
Example 4
Input
```
G 2
G 3
Y ....
```
Expected output
```
David Paul Jack Alex
```
Example 5
Input
```
W .
B 2
W III
```
Expected output
```
Robert Mark
```