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.*;
import java.util.*;
 
	 
	 
	public   class Main {
		private InputStream is;
		private PrintWriter out;
		int time = 0, val[][], dp[][], DP[], start[], end[], dist[],  black[], MOD = (int)(1e9+7), arr[], weight[][], x[], y[], parent[];
		int MAX = 800000, N, K;
		long red[];
		ArrayList<Integer>[] amp;
		ArrayList<Pair>[][] pmp;
		boolean b[], boo[][];
		Pair prr[];
		HashMap<Integer,Long> hm[] = new HashMap[305];
		long Dp[][][][] = new long[110][110][12][12];
		void soln() {
			is = System.in;
			out = new PrintWriter(System.out);
			long s = System.currentTimeMillis();
			solve();
			//out.close();
			out.flush();
			//tr(System.currentTimeMillis() - s + "ms");
		}
		public static void main(String[] args) throws Exception {
			new Thread(null, new Runnable() {
			public void run() {
				try {
			//new CODEFORCES().soln();
			} catch (Exception e) {
					System.out.println(e);
				}
			}
		}, "1", 1 << 26).start();
			new Main().soln();
		}
		int ans = 0, cost = 0;
		char ch[], ch1[];
		void solve(){
			char ch1 = ns().charAt(0), ch2 = ns().charAt(0);
			int n = ni();
			int y = n%4;
			if(y==0 || y==2){
					System.out.println("undefined");
					return;
			}
			else if(y==1){
				if(ch1=='^'){
					if(ch2=='>'){
						System.out.println("cw");
					}
					else if(ch2=='<') System.out.println("ccw");
					else System.out.println("undefined");
					return;
				}
				else if(ch1=='>'){
					if(ch2=='v'){
						System.out.println("cw");
					}
					else if(ch2=='^') System.out.println("ccw");
					else System.out.println("undefined");
					return;
				}
				else if(ch1=='<'){
					if(ch2=='^'){
						System.out.println("cw");
					}
					else if(ch2=='v') System.out.println("ccw");
					else System.out.println("undefined");
					return;
				}
				else if(ch1=='v'){
					if(ch2=='<'){
						System.out.println("cw");
					}
					else if(ch2=='>') System.out.println("ccw");
					else System.out.println("undefined");
					return;
				}
			}
			else{
				if(ch1=='^'){
					if(ch2=='<'){
						System.out.println("cw");
					}
					else if(ch2=='>') System.out.println("ccw");
					else System.out.println("undefined");
					return;
				}
				else if(ch1=='>'){
					if(ch2=='^'){
						System.out.println("cw");
					}
					else if(ch2=='v') System.out.println("ccw");
					else System.out.println("undefined");
					return;
				}
				else if(ch1=='<'){
					if(ch2=='v'){
						System.out.println("cw");
					}
					else if(ch2=='^') System.out.println("ccw");
					else System.out.println("undefined");
					return;
				}
				else if(ch1=='v'){
					if(ch2=='>'){
						System.out.println("cw");
					}
					else if(ch2=='<') System.out.println("ccw");
					else System.out.println("undefined");
					return;
				}
			}
		}
		void sieve(int n){
			b = new boolean[n+1];
			b[0] = b[1] = true;
			for(int i = 2;i*i<n;i++){
				if(!b[i]){
					for(int j = 2*i;j<100001;j+=i) b[j] = true;
				}
			}
		}
		class Pair implements Comparable<Pair>{
			int u, v, i;
			
			Pair(int u, int v){
				this.u = u;
				this.v = v;
			}
			Pair(){
				
			}
			Pair(int u, int v, int i){
				this.u = u;
				this.v = v;
				this.i = i;
			}
			public int hashCode() {
				return Objects.hash();
			}
			public boolean equals(Object o) {
				Pair other = (Pair) o;
				return ((u == other.u && v == other.v)); 
			}
			public int compareTo(Pair other) {
				//return Integer.compare(val, other.val);
				return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)) : (Long.compare(v,other.v));
			}
			public String toString(){
				return this.u +" " + this.v;
			}
		}
		int max(int a, int b){
			if(a>b) return a;
			return b;
		}
		public static class FenwickTree {
			
		    int[] array; // 1-indexed array, In this array We save cumulative information to perform efficient range queries and updates
	 
		    public FenwickTree(int size) {
		        array = new int[size + 1];
		    }
		    public int rsq(int ind) {
		        assert ind > 0;
		        int sum = 0;
		        while (ind > 0) {
		            sum += array[ind];
		            //Extracting the portion up to the first significant one of the binary representation of 'ind' and decrementing ind by that number
		            ind -= ind & (-ind);
		        }
		        return sum;
		    }
		    public int rsq(int a, int b) {
		        assert b >= a && a > 0 && b > 0;
		        return rsq(b) - rsq(a - 1);
		    }
		    public void update(int ind, int value) {
		        assert ind > 0;
		        while (ind < array.length) {
		            array[ind] += value;
		            //Extracting the portion up to the first significant one of the binary representation of 'ind' and incrementing ind by that number
		            ind += ind & (-ind);
		        }
		    }
		    public int size() {
		        return array.length - 1;
		    }
		}
		void buildGraph(int n){
			for(int i = 0; i<n ;i++){
				int x1 = ni() -1, y1 = ni()-1;
				amp[x1].add(y1);
				amp[y1].add(x1);
				x[i] = x1; y[i] = y1;
			}
		}
		long modInverse(long a, long mOD2){
	        return  power(a, mOD2-2, mOD2);
		}
		long power(long x, long y, long m)
		{
			if (y == 0)
	    return 1;
		long p = power(x, y/2, m) % m;
		p = (p * p) % m;
	 
		return (y%2 == 0)? p : (x * p) % m;
		}
		public int gcd(int a, int b){
			if(b==0) return a;
			return gcd(b,a%b);
		}
		static class ST1{
			int arr[], st[], size;
			ST1(int a[]){
				arr = a.clone();
				size = 10*arr.length;
				st = new int[size];
				build(0,arr.length-1,1);
			}
			void build(int ss, int se, int si){
				if(ss==se){
					st[si] = arr[ss];
					return;
				}
				int mid = (ss+se)/2;
				int val = 2*si;
				build(ss,mid,val); build(mid+1,se,val+1);
				st[si] = Math.min(st[val], st[val+1]);
			}
			int get(int ss, int se, int l, int r, int si){
				if(l>se || r<ss || l>r) return Integer.MAX_VALUE;
				if(l<=ss && r>=se) return st[si];
				int mid = (ss+se)/2;
				int val = 2*si;
				return Math.min(get(ss,mid,l,r,val), get(mid+1,se,l,r,val+1));
			}
		}
		static class ST{
			int arr[],lazy[],n;
			ST(int a){
				n = a;
				arr = new int[10*n];
				lazy = new int[10*n];
			}
			void up(int l,int r,int val){
				update(0,n-1,0,l,r,val);
			}
			void update(int l,int r,int c,int x,int y,int val){
				if(lazy[c]!=0){
					lazy[2*c+1]+=lazy[c];
					lazy[2*c+2]+=lazy[c];
					if(l==r)
						arr[c]+=lazy[c];
					lazy[c] = 0;
				}
				if(l>r||x>y||l>y||x>r)
					return;
				if(x<=l&&y>=r){
					lazy[c]+=val;
					return ;
				}
				int mid = l+r>>1;
				update(l,mid,2*c+1,x,y,val);
				update(mid+1,r,2*c+2,x,y,val);
				arr[c] = Math.max(arr[2*c+1], arr[2*c+2]);
			}
			int an(int ind){
				return ans(0,n-1,0,ind);
			}
			int ans(int l,int r,int c,int ind){
				if(lazy[c]!=0){
					lazy[2*c+1]+=lazy[c];
					lazy[2*c+2]+=lazy[c];
					if(l==r)
						arr[c]+=lazy[c];
					lazy[c] = 0;
				}
				if(l==r)
					return arr[c];
				int mid = l+r>>1;
				if(mid>=ind)
					return ans(l,mid,2*c+1,ind);
				return ans(mid+1,r,2*c+2,ind);
			}
		}
		public static int[] shuffle(int[] a, Random gen){
			for(int i = 0, n = a.length;i < n;i++)
			{ 
				int ind = gen.nextInt(n-i)+i; 
				int d = a[i]; 
				a[i] = a[ind];
				a[ind] = d; 
			} 
		return a; 
		}
		long power(long x, long y, int mod){
			long ans = 1;
			while(y>0){
				if(y%2==0){
					x = (x*x)%mod;
					y/=2;
				}
				else{
					ans = (x*ans)%mod;
					y--;
				}
			}
			return ans;
		}
	 
	 
		// To Get Input
		// Some Buffer Methods
		private byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;
	 
		private int readByte() {
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) {
				ptrbuf = 0;
				try {
					lenbuf = is.read(inbuf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}
	 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
	 
		private int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}
	 
		private double nd() {
			return Double.parseDouble(ns());
		}
	 
		private char nc() {
			return (char) skip();
		}
		private String ns() {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != '
										// ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
	 
		private char[] ns(int n) {
			char[] buf = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) {
				buf[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buf : Arrays.copyOf(buf, p);
		}
	 
		private char[][] nm(int n, int m) {
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = ns(m);
			return map;
		}
	 
		private int[] na(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = ni();
			return a;
		}
	 
		private int ni() {
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
	 
			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	 
		private long nl() {
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
	 
			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	 
		private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	 
		private void tr(Object... o) {
			if (!oj)
				System.out.println(Arrays.deepToString(o));
		}
	}