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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.OptionalInt;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;
import java.util.stream.Collectors;

public class Solution implements Runnable
{
    private void solve() throws IOException
    {
    	//max_int > 2 * 10^9
    	
    	String s = nextToken();
    	String e = nextToken();
    	int n = nextInt(); 
    	
    	if (n % 2 == 0) {
    		writer.print("undefined");
    	}
    	else {
    		int x = n % 4;
    		if (x == 1) {
    			if (s.equals("^")) {
    				if (e.equals(">")) {
    		    		writer.print("cw");
    				}
    				else {
    					writer.print("ccw");
    				}
    			}
    			else if (s.equals(">")) {
    				if (e.equals("v")) {
    		    		writer.print("cw");
    				}
    				else {
    					writer.print("ccw");
    				}
    			}
    			else if (s.equals("v")) {
    				if (e.equals("<")) {
    		    		writer.print("cw");
    				}
    				else {
    					writer.print("ccw");
    				}
    			}
    			else if (s.equals("<")) {
    				if (e.equals("^")) {
    		    		writer.print("cw");
    				}
    				else {
    					writer.print("ccw");
    				}
    			}
    		}
    		else if (x == 3) {
    			if (s.equals("^")) {
    				if (e.equals("<")) {
    		    		writer.print("cw");
    				}
    				else {
    					writer.print("ccw");
    				}
    			}
    			else if (s.equals(">")) {
    				if (e.equals("^")) {
    		    		writer.print("cw");
    				}
    				else {
    					writer.print("ccw");
    				}
    			}
    			else if (s.equals("v")) {
    				if (e.equals(">")) {
    		    		writer.print("cw");
    				}
    				else {
    					writer.print("ccw");
    				}
    			}
    			else if (s.equals("<")) {
    				if (e.equals("v")) {
    		    		writer.print("cw");
    				}
    				else {
    					writer.print("ccw");
    				}
    			}
    		}
    	}
    	
  
    	
    	
    	
    }
    
    private List<Integer> primeFact(int n) {
	     List<Integer> factors = new ArrayList<Integer>();
	     
	     for (int i = 2; i <= n / i; i++) {
             while (n % i == 0) {
                 factors.add(i);
                 n /= i;
             }
	     }
	     if (n > 1) 
	    	 factors.add(n);
	     
	     return factors.stream().distinct().collect(Collectors.toList());
    }
    
    private List<Integer> findPrimes(int n)
    {
        boolean prime[] = new boolean[n+1];
        for(int i=0;i<n;i++)
            prime[i] = true;
         
        for(int p = 2; p*p <=n; p++)
        {
            if(prime[p] == true)
            {
                for(int i = p*2; i <= n; i += p)
                    prime[i] = false;
            }
        }
        
        List<Integer> list = new ArrayList<Integer>();
        for(int i = 2; i <= n; i++)
        {
            if(prime[i] == true)
            	list.add(i);
        }
        
        return list;
        
    }
    
    private List<Long> fact(long n)
    {
     TreeSet<Long> factors = new TreeSet<Long>();
     
     factors.add(n);
     factors.add(1L);
     
     for(long i = n - 1; i >= Math.sqrt(n); i--)
	      if(n % i == 0)
	      {
	       factors.add(i);
	       factors.add(n / i);
	      }
     
     return factors.stream().collect(Collectors.toList());
    }
    
    private String minFact(long n) {
    	String str = 1 + " " + n;
	     long min = Long.MAX_VALUE;
	     for(long i = n - 1; i >= Math.sqrt(n); i--)
		      if(n % i == 0) {
		    	  long x = i - n/i;
		    	  
		    	  if (x < min) {
		    		  min = x;
		    		  str = n/i + " " + i;
		    	  }
		       
		      }
	     
	     return str;
    }
    
    private long gcd (long a, long b) {
        BigInteger b1 = BigInteger.valueOf(a);
        BigInteger b2 = BigInteger.valueOf(b);
         
        return b1.gcd(b2).longValue();
    }
    
    private long lcm (long a, long b, long gcd) {
    	return a * b / gcd;
    }
        
    private boolean isPowerOfTwo(long x) {
        return (x != 0) && ((x & (x - 1)) == 0);
    }
    
    private int exponentOfTwo(long n) {
    	return (int)( Math.floor(Math.log(n) / Math.log(2)));

    }

    private Long sumDiagLR (Long[][] array) {
        long sum = 0;
        int i = 0, j = 0;

        while (i < array.length && j < array.length) {
            sum += array[i][j];
            i++;
            j++;
        }

        return sum;
    }

    private Long sumDiagRL (Long[][] array) {
       long sum = 0;
       int i = array.length-1, j = 0;

       while (i >=0 && j < array.length) {
           sum += array[i][j];
           i--;
           j++;
       }

       return sum;
   }


    private BigInteger factorial( String n )
    {
        BigInteger k = new BigInteger( n );
        BigInteger ans = BigInteger.ONE;

        while ( k.compareTo( BigInteger.ONE ) > 0 )
        {
            ans = ans.multiply( k );
            k = k.subtract( BigInteger.ONE );
        }

        return ans;
    }

    private long combinations( long n, long r )
    {
        return ( factorial( String.valueOf( n ) ).divide( ( new BigInteger( String.valueOf( r ) ).multiply( factorial( String.valueOf( n - r ) ) ) ) ) ).longValue();
    }


    private String binaryXOR( String s1, String s2 )
    {
        BigInteger a = new BigInteger( s1, 2 );
        BigInteger b = new BigInteger( s2, 2 );

        return a.xor( b ).toString( 2 );

    }


    private static void findDP( Node node )
    {
        for ( Node child : node.children )
        {
            if ( child.value > node.value )
            {
                child.dp = Math.max( child.dp, node.dp + 1 );
                //findDP( child );
            }
        }
    }

    private static class Obj implements Comparable<Obj>
    {
        String name;
        int value;

        public Obj( int value )
        {
            this.value = value;
        }

        public Obj( String name, int value )
        {
            this.name = name;
            this.value = value;
        }

        @Override
        public int compareTo( Obj o )
        {
            return o.value - this.value;
        }
    }


    private static class Edge
    {
        PNode src;
        PNode des;
        long cost;

        public Edge (PNode src, PNode des, long cost) {
            this.src = src;
            this.des = des;
            this.cost = cost;
        }
    }

    private static class PNode
    {
        List<Edge> edges;
        long value;
        boolean isTrue;

        public PNode() {
            this.edges = new ArrayList<>(  );
            this.isTrue = false;
        }

        public PNode(long value ) {
           this.edges = new ArrayList<>(  );
           this.isTrue = false;
            this.value = value;
       }
    }

    private static class Node
    {
        long value;
        long dp;
        List<Node> children;
        Node parent;

        public  Node(){};

        public Node( int value )
        {
            this.value = value;
            dp = 1;
            children = new ArrayList<Node>();
        }
    }

    private static boolean isInt( String s )
    {
        if ( s.length() < 1 )
            return false;
        else
        {
            for ( char c : s.toCharArray() )
            {
                if ( c < '0' || c > '9' )
                {
                    return false;
                }
            }
        }

        return true;
    }

    private static Map<String, Integer> findSubString( String s, int k )
    {
        Map<String, Integer> map = new HashMap<>();
        for ( int i = 0; i < s.length() - ( k - 1 ); i++ )
        {
            String str = new String( s.substring( i, i + k ) );
            if ( map.containsKey( str ) )
            {
                map.put( str, map.get( str ) + 1 );
            }
            else
            {
                map.put( str, 1 );

            }
        }

        return map;
    }


    //mergesort

    public static Comparable[] mergeSort( Comparable[] list )
    {
        if ( list.length <= 1 )
        {
            return list;
        }

        Comparable[] left = new Comparable[ list.length / 2 ];
        Comparable[] right = new Comparable[ list.length - left.length ];
        System.arraycopy( list, 0, left, 0, left.length );
        System.arraycopy( list, left.length, right, 0, right.length );

        mergeSort( left );
        mergeSort( right );

        merge( left, right, list );
        return list;
    }

    private static void merge( Comparable[] left, Comparable[] right, Comparable[] result )
    {
        int leftIdx = 0;
        int rightIdx = 0;
        int index = 0;

        while ( leftIdx < left.length && rightIdx < right.length )
        {
            if ( left[ leftIdx ].compareTo( right[ rightIdx ] ) < 0 )
            {
                result[ index++ ] = left[ leftIdx ];
                leftIdx++;
            }
            else
            {
                result[ index++ ] = right[ rightIdx ];
                rightIdx++;
            }
        }

        System.arraycopy( left, leftIdx, result, index, left.length - leftIdx );
        System.arraycopy( right, rightIdx, result, index, right.length - rightIdx );
    }

    public static List<Obj> mergeSort( List<Obj> list )
    {
        if ( list.size() <= 1 )
        {
            return list;
        }

        List<Obj> left = new ArrayList( list.subList( 0, list.size() / 2 ) );
        List<Obj> right = new ArrayList( list.subList( left.size(), list.size() ) );

        left = mergeSort( left );
        right = mergeSort( right );

        list = merge( left, right );

        return list;
    }

    private static List<Obj> merge( List<Obj> left, List<Obj> right )
    {
        int leftCounter = 0, rightCounter = 0;
        List<Obj> result = new ArrayList<>();

        while ( leftCounter < left.size() && rightCounter < right.size() )
        {
            Obj leftItem = left.get( leftCounter );
            Obj rightItem = right.get( rightCounter );

            if ( leftItem.compareTo( rightItem ) < 0 )
            {
                result.add( leftItem );
                leftCounter++;
            }
            else
            {
                result.add( rightItem );
                rightCounter++;
            }
        }

        if ( leftCounter >= left.size() )
            result.addAll( right.subList( rightCounter, right.size() ) );
        else if ( rightCounter >= right.size() )
            result.addAll( left.subList( leftCounter, left.size() ) );

        return result;
    }

    public static void main( String[] args )
    {
        new Solution().run();
    }

    BufferedReader reader;
    StringTokenizer tokenizer;
    PrintWriter writer;

    public void run()
    {
        try
        {
            reader = new BufferedReader( new InputStreamReader( System.in ) );
            tokenizer = null;
            writer = new PrintWriter( System.out );
            solve();
            reader.close();
            writer.close();
        }
        catch ( Exception e )
        {
            e.printStackTrace();
            System.exit( 1 );
        }
    }

    int nextInt() throws IOException
    {
        return Integer.parseInt( nextToken() );
    }

    long nextLong() throws IOException
    {
        return Long.parseLong( nextToken() );
    }

    double nextDouble() throws IOException
    {
        return Double.parseDouble( nextToken() );
    }

    String nextToken() throws IOException
    {
        while ( tokenizer == null || !tokenizer.hasMoreTokens() )
        {
            tokenizer = new StringTokenizer( reader.readLine() );
        }
        return tokenizer.nextToken();
    }
    
    public class Tuple {
    	Object fst;
    	Object snd;
    	
    	public Tuple(Object fst, Object snd) {
    		this.fst = fst;
    		this.snd = snd;
    	}
    	
    	public Object getFst() {
    		return fst;
    	}
    	
    	public Object getSnd() {
    		return snd;
    	}
    	
    }

    // Arrays.sort(array, Comparator.comparing((int[] arr) -> arr[1]));
}