Problem: <image>

Walking through the streets of Marshmallow City, Slastyona have spotted some merchants selling a kind of useless toy which is very popular nowadays – caramel spinner! Wanting to join the craze, she has immediately bought the strange contraption.

Spinners in Sweetland have the form of V-shaped pieces of caramel. Each spinner can, well, spin around an invisible magic axis. At a specific point in time, a spinner can take 4 positions shown below (each one rotated 90 degrees relative to the previous, with the fourth one followed by the first one):

<image>

After the spinner was spun, it starts its rotation, which is described by a following algorithm: the spinner maintains its position for a second then majestically switches to the next position in clockwise or counter-clockwise order, depending on the direction the spinner was spun in.

Slastyona managed to have spinner rotating for exactly n seconds. Being fascinated by elegance of the process, she completely forgot the direction the spinner was spun in! Lucky for her, she managed to recall the starting position, and wants to deduct the direction given the information she knows. Help her do this.

Input

There are two characters in the first string – the starting and the ending position of a spinner. The position is encoded with one of the following characters: v (ASCII code 118, lowercase v), < (ASCII code 60), ^ (ASCII code 94) or > (ASCII code 62) (see the picture above for reference). Characters are separated by a single space.

In the second strings, a single number n is given (0 ≤ n ≤ 109) – the duration of the rotation.

It is guaranteed that the ending position of a spinner is a result of a n second spin in any of the directions, assuming the given starting position.

Output

Output cw, if the direction is clockwise, ccw – if counter-clockwise, and undefined otherwise.

Examples

Input

^ &gt;
1


Output

cw


Input

&lt; ^
3


Output

ccw


Input

^ v
6


Output

undefined

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.Locale;
import java.util.Scanner;
import java.util.regex.Pattern;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.UnsupportedEncodingException;
import java.math.BigInteger;

public class TheUselessToy {

	public static int[] pattern = {94, 62, 118, 60};
	
	public static void main(String[] args) {

		solve(1);

	}
	
	public static void solve(int testCases){
		String s1 = StdIn.readString();
		String s2 = StdIn.readString();
		char src = s1.charAt(0);
		char dest = s2.charAt(0);
		//StdOut.println("src = " + src + " dest = " + dest);
		int n = StdIn.readInt();
		int d1 = clockWise(src, n);
		int d2 = anticlockWise(src, n);
		char cd1 = (char) d1;
		char cd2 = (char) d2;
		if(cd1 == dest && cd2 != dest){
			StdOut.println("cw");
		}else if(cd1 != dest && cd2 == dest){
			StdOut.println("ccw");
		}else{
			StdOut.println("undefined");
		}
	}
	
	public static int clockWise(char src, int n){
		int t = src;
		for(int i = 0 ; i < 4 ; i++)
			if(t == pattern[i])
				t = i;
		int r = n % 4;
		t += r;
		t = t % 4;
		return pattern[t];
	}

	public static int anticlockWise(char src, int n){
		int t = src;
		for(int i = 0 ; i < 4 ; i++)
			if(t == pattern[i])
				t = i;
		int r = n % 4;
		t -= r;
		if(t < 0)
			t += 4;
		return pattern[t];
	}

}

final class StdIn {
 
    private StdIn() { }
 
    private static Scanner scanner;
    
    private static final String CHARSET_NAME = "UTF-8";
 
    private static final Locale LOCALE = Locale.US;
 
    private static final Pattern WHITESPACE_PATTERN = Pattern.compile("\\p{javaWhitespace}+");
 
    private static final Pattern EMPTY_PATTERN = Pattern.compile("");
 
    private static final Pattern EVERYTHING_PATTERN = Pattern.compile("\\A");
 
    public static boolean isEmpty() {
        return !scanner.hasNext();
    }
 
    public static boolean hasNextLine() {
        return scanner.hasNextLine();
    }
 
    public static boolean hasNextChar() {
        scanner.useDelimiter(EMPTY_PATTERN);
        boolean result = scanner.hasNext();
        scanner.useDelimiter(WHITESPACE_PATTERN);
        return result;
    }
 
    public static String readLine() {
        String line;
        try                 { line = scanner.nextLine(); }
        catch (Exception e) { line = null;               }
        return line;
    }
 
    public static char readChar() {
        scanner.useDelimiter(EMPTY_PATTERN);
        String ch = scanner.next();
        assert (ch.length() == 1) : "Internal (Std)In.readChar() error!"
            + " Please contact the authors.";
        scanner.useDelimiter(WHITESPACE_PATTERN);
        return ch.charAt(0);
    }  
 
 
    public static String readAll() {
        if (!scanner.hasNextLine())
            return "";
 
        String result = scanner.useDelimiter(EVERYTHING_PATTERN).next();
        // not that important to reset delimeter, since now scanner is empty
        scanner.useDelimiter(WHITESPACE_PATTERN); // but let's do it anyway
        return result;
    }
 
    public static String readString() {
        return scanner.next();
    }
 
    public static int readInt() {
        return scanner.nextInt();
    }
 
    public static double readDouble() {
        return scanner.nextDouble();
    }
 
    public static float readFloat() {
        return scanner.nextFloat();
    }
 
    public static long readLong() {
        return scanner.nextLong();
    }
    
    public static short readShort() {
        return scanner.nextShort();
    }
 
    public static byte readByte() {
        return scanner.nextByte();
    }
 
    public static boolean readBoolean() {
        String s = readString();
        if (s.equalsIgnoreCase("true"))  return true;
        if (s.equalsIgnoreCase("false")) return false;
        if (s.equals("1"))               return true;
        if (s.equals("0"))               return false;
        throw new InputMismatchException();
    }
 
    public static String[] readAllStrings() {
        // we could use readAll.trim().split(), but that's not consistent
        // because trim() uses characters 0x00..0x20 as whitespace
        String[] tokens = WHITESPACE_PATTERN.split(readAll());
        if (tokens.length == 0 || tokens[0].length() > 0)
            return tokens;
 
        // don't include first token if it is leading whitespace
        String[] decapitokens = new String[tokens.length-1];
        for (int i = 0; i < tokens.length - 1; i++)
            decapitokens[i] = tokens[i+1];
        return decapitokens;
    }
 
    public static String[] readAllLines() {
        ArrayList<String> lines = new ArrayList<String>();
        while (hasNextLine()) {
            lines.add(readLine());
        }
        return lines.toArray(new String[0]);
    }
 
    public static int[] readAllInts() {
        String[] fields = readAllStrings();
        int[] vals = new int[fields.length];
        for (int i = 0; i < fields.length; i++)
            vals[i] = Integer.parseInt(fields[i]);
        return vals;
    }
 
    public static double[] readAllDoubles() {
        String[] fields = readAllStrings();
        double[] vals = new double[fields.length];
        for (int i = 0; i < fields.length; i++)
            vals[i] = Double.parseDouble(fields[i]);
        return vals;
    }
    
    static {
        resync();
    }
 
    private static void resync() {
        setScanner(new Scanner(new java.io.BufferedInputStream(System.in), CHARSET_NAME));
    }
    
    private static void setScanner(Scanner scanner) {
        StdIn.scanner = scanner;
        StdIn.scanner.useLocale(LOCALE);
    }
 
    public static int[] readInts() {
        return readAllInts();
    }
 
    public static double[] readDoubles() {
        return readAllDoubles();
    }
 
    public static String[] readStrings() {
        return readAllStrings();
    }
 
}
 
final class StdOut {
 
    private static final String CHARSET_NAME = "UTF-8";
 
    private static final Locale LOCALE = Locale.US;
 
    private static PrintWriter out;
 
    static {
        try {
            out = new PrintWriter(new OutputStreamWriter(System.out, CHARSET_NAME), true);
        }
        catch (UnsupportedEncodingException e) { System.out.println(e); }
    }
 
    private StdOut() { }
 
    public static void close() {
        out.close();
    }
 
    public static void println() {
        out.println();
    }
 
    public static void println(Object x) {
        out.println(x);
    }
 
    public static void println(boolean x) {
        out.println(x);
    }
 
    public static void println(char x) {
        out.println(x);
    }
 
    public static void println(double x) {
        out.println(x);
    }
 
    public static void println(float x) {
        out.println(x);
    }
 
    public static void println(int x) {
        out.println(x);
    }
 
    public static void println(long x) {
        out.println(x);
    }
 
    public static void println(short x) {
        out.println(x);
    }
 
    public static void println(byte x) {
        out.println(x);
    }
 
    public static void print() {
        out.flush();
    }
 
    public static void print(Object x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(boolean x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(char x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(double x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(float x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(int x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(long x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(short x) {
        out.print(x);
        out.flush();
    }
 
    public static void print(byte x) {
        out.print(x);
        out.flush();
    }
 
    public static void printf(String format, Object... args) {
        out.printf(LOCALE, format, args);
        out.flush();
    }
 
    public static void printf(Locale locale, String format, Object... args) {
        out.printf(locale, format, args);
        out.flush();
    }
 
}