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:
// AUTHOR : MAYANK SUNAL

import java.io.*;
import java.util.*;
import java.math.*;

public class Main {
	static final Random random = new Random();
	static PrintWriter out = new PrintWriter((System.out));
	static Reader sc = new Reader();

	public static void main(String args[]) throws IOException {
//		int t = sc.nextInt();
//		while (t-- > 0) {
//        	CODE START FROM HERE long n = sc.nextLong();
		char a = sc.next().charAt(0);
		char b = sc.next().charAt(0);
		int n = sc.nextInt();
		Integer arr[] = { 118, 60, 94, 62 };
		int index = 0;
		for (int i = 0; i < 4; i++)
			if (arr[i] == (int) a) {
				index = i;
				break;
			}
		if (arr[(index + (n % 4)) % 4] == (int) b && arr[(4 + index - (n % 4)) % 4] == (int) b)
			System.out.println("undefined");
		else if (arr[(4 + index - (n % 4)) % 4] == (int) b)
			System.out.println("ccw");
		else if (arr[(index + (n % 4)) % 4] == (int) b)
			System.out.println("cw");

//		}

	}

// Fast Input Output
	static class Reader {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");

		public String next() {
			while (!st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public String nextLine() {
			try {
				return br.readLine();
			} catch (Exception e) {
				e.printStackTrace();
			}
			return null;
		}

		public boolean hasNext() {
			String next = null;
			try {
				next = br.readLine();
			} catch (Exception e) {
			}
			if (next == null) {
				return false;
			}
			st = new StringTokenizer(next);
			return true;
		}

	}

	// EFFICIENT SORTING Ascending
	static void ruffleSortAsc(Integer[] a) {
		int n = a.length; // shuffle, then sort
		for (int i = 0; i < n; i++) {
			int oi = random.nextInt(n), temp = a[oi];
			a[oi] = a[i];
			a[i] = temp;
		}
		Arrays.sort(a);
	}

//	EFFICIENT SORTING Descending
	static void ruffleSortDesc(Integer[] a) {
		int n = a.length; // shuffle, then sort
		for (int i = 0; i < n; i++) {
			int oi = random.nextInt(n), temp = a[oi];
			a[oi] = a[i];
			a[i] = temp;
		}
		Arrays.sort(a, Collections.reverseOrder());
	}

	// Array Sum
	static long sum(Integer[] arr) {
		long sum = 0;
		for (int i : arr)
			sum += i;
		return sum;
	}

	// ArrayList Sum
	static long sumal(ArrayList<Integer> al) {
		long sum = 0;
		for (int i : al)
			sum += i;
		return sum;
	}

	// swap array elements
	static void swap(int arr1[], int arr2[], int i, int j) {
		int temp = arr1[i];
		arr1[i] = arr2[j];
		arr2[j] = temp;
	}

	// reading array value;
	static void read(Integer[] arr) {
		for (int i = 0; i < arr.length; i++)
			arr[i] = sc.nextInt();
		return;
	}

//    reading arraylistValue

	static void readal(List<Integer> l, int n) {
		for (int i = 0; i < n; i++)
			l.add(sc.nextInt());
		return;
	}

	// check for even odd
	static boolean isEven(long n) {
		return ((n & 1) != 1);
	}

	// max in a array
	static int max(Integer[] arr) {
		int max = Integer.MIN_VALUE;
		for (int i = 0; i < arr.length; i++)
			if (max < arr[i])
				max = arr[i];
		return max;
	}

//  print array
	static void printarr(Integer arr[]) {
		for (int i : arr)
			System.out.println(i);
	}

// ceil of two elements
	static int ceil(int a, int b) {
		return (int) Math.ceil(((double) a / (double) b));
	}

// floor of two elements
	static int floor(int a, int b) {
		return (int) Math.floor(((double) a / (double) b));
	}
}