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 com.sun.corba.se.impl.orbutil.ORBConstants;
import java.io.PrintWriter;

import java.util.*;
import java.util.Arrays ; 

 
import java.io.DataInputStream; 
import java.io.FileInputStream; 
import java.io.IOException; 
import java.lang.reflect.Array;


public class Test{
     static PrintWriter  pw = new PrintWriter(System.out); 
static class Reader 
    { 
    
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 
   

static int find(long x[],long r){
    int sum =0 ;
    
    for (int i = 0; i < x.length; i++) {
        if(x[i]==r) return i+1 ;
    }
    return sum ;
}
static int [] find2(int x[][],int temp,int y[]){
    for (int i = 0; i < x.length; i++) {
        int sum=0 ;
        for (int j = 0; j < x.length; j++) {
           sum+=x[j][i] ;
        }
        y[i]=sum ;
   
    }
   return y;
    
}
static void found(LinkedList<Integer> l1,String s,LinkedList<Integer> l2){
    for (int i = 0; i < s.length()-1; i++) {
        String temp ="" ;
                temp +=(char)s.charAt(i);
                temp +=(char)s.charAt(i+1);
        if(temp.equals("AB"))l1.add(i) ;
        if(temp.equals("BA"))l2.add(i) ;
    }
}
 static String db(String s){
     StringBuilder b= new StringBuilder(s) ;
     
     return s+(b.reverse().toString()) ; 
    
 }
 static String btw(String s,char c){
     StringBuilder b= new StringBuilder(s) ;
     
     return (s+c)+(b.reverse().toString()) ; 
    
 }

      
      
            


    public static void main(String[] args) throws IOException  {

    
        
  // Reader  in =new Reader ();
  Scanner  in =new Scanner (System.in);
  String s= in.nextLine(); 
       // System.out.println(s.charAt(2));   
  long n = in.nextLong() ; 
  int t =0 ; 
  if(s.charAt(0)==118) t=1 ;
  if(s.charAt(0)==60)t= 2 ; 
  if(s.charAt(0)==94)t= 3 ; 
  if(s.charAt(0)==62)t= 4 ;
  long save= ((t+n)%4) ;
  if((t+n)%4==0)save=4 ;
  char o ='e' ;
  if(save==1)o=118 ;
  if(save==2)o=60 ; 
  if(save==3)o=94 ;
  if(save==4)o=62 ;
        
  if(s.charAt(0)==118) t=4 ;
  if(s.charAt(0)==60)t= 3 ; 
  if(s.charAt(0)==94)t= 2 ; 
  if(s.charAt(0)==62)t= 1 ;
   save= ((t+n)%4) ;
   if((t+n)%4==0)save=4 ;
   char o2='f' ;
  if(save==4)o2=118 ;
  if(save==3)o2=60 ; 
  if(save==2)o2=94 ;
  if(save==1)o2=62 ;
 // System.out.println(o2);
  if(o==s.charAt(2)&&o2==s.charAt(2)){
      System.out.println("undefined");
      return ;
  }
  if(o==s.charAt(2)){
      System.out.println("cw");   
  }else {
      System.out.println
        ("ccw");
  }
        pw.close();
}
}