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.util.*;

public class Codeforces {

    private static final Scanner sc = new Scanner(System.in);
    private static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private static final long MOD = (long) (1e9 + 7);

    public static int[] LPS(String p){
        int[] lps = new int[p.length()];

        int i=1;
        int j=0;
        while (i < p.length()){
            if (p.charAt(i) == p.charAt(j)){
                lps[i] = j+1;
                i++;
                j++;
            }
            else{
                if (j == 0){
                    lps[i] = 0;
                    i++;
                }
                else{
                    j = lps[j-1];
                }
            }
        }
        return lps;
    }

    public static void KMP(String text,String pattern){
        int[] lps = LPS(pattern);
        int i = 0;
        int j = 0;
        ArrayList<Integer> matches = new ArrayList<>();
        while (i < text.length()){
            if (text.charAt(i) == pattern.charAt(j)){
                i++;
                j++;
            }
            else{
                if (j != 0){
                    j = lps[j-1];
                }
                else {
                    i++;
                }
            }
            if (j == pattern.length()) {
                matches.add(i - j);
                j = lps[j-1];
            }
        }
        for (int x : matches){
            System.out.println("Match at : " + x);
        }
    }

    private static class SegmentTree{
        private long[] st;
        private int size;
        private int n;
        private long[] a;
        SegmentTree(long[] a,int n){
            this.size = 4*n;
            this.n = n;
            this.a = a;
            st = new long[size];
            //Arrays.fill(st,Integer.MIN_VALUE);
            buildSegmentTree(0,0,n-1);
            //printSegmentTree();
        }
        public long buildSegmentTree(int index,int l,int r){
            if (l == r){
                st[index] = a[l];
                return a[l];
            }
            int mid = (r+l) >> 1;
            return st[index] = buildSegmentTree(2*index+1,l,mid) + buildSegmentTree(2*index+2,mid+1,r);
        }
        public void printSegmentTree(){
            for (long x : st){
                System.out.print(x + " ");
            }
            System.out.println();
        }
        public long query(int ql,int qr){
            return getQuery(0,0,n-1,ql-1,qr-1);
        }
        private long getQuery(int index,int sl,int sr,int ql,int qr){
            //System.out.println("#" + index);
            if (qr < sl || ql > sr)
                return 0;
            if (ql <= sl && qr >= sr)
                return st[index];
            int mid = (sr + sl) >> 1;
            return getQuery(2*index+1,sl,mid,ql,qr) + getQuery(2*index+2,mid+1,sr,ql,qr);
        }
        public void update(int i,long newVal){
            //long diff = newVal - a[i];
            a[i] = newVal;
            updateSegmentTree(0,i,0,n-1,newVal);
        }
        private void updateSegmentTree(int index,int i,int sl,int sr,long diff){
            if (sl == sr){
                st[index] = diff;
                return;
            }
            int mid = (sl + sr) >> 1;
            if (i <= mid)
                updateSegmentTree(2*index+1,i,sl,mid,diff);
            else
                updateSegmentTree(2*index+2,i,mid+1,sr,diff);
            st[index] = st[2*index+1] + st[2*index+2];
        }
    }

    public static class Pair<T1,T2>{
        T1 first;
        T2 second;
        Pair(T1 a,T2 b){
            this.first = a;
            this.second = b;
        }

        @Override
        public String toString() {
            return "[" + first + ", " + second + "]";
        }
    }

    public static long GCD(long a,long b){
        if (b == 0)
            return a;
        return GCD(b,a%b);
    }

    static int highestPowerOf2(int n) {
        int p = (int)(Math.log(n) /
                Math.log(2));
        return (int)Math.pow(2, p);
    }

    public static int binSearch(long[] a,long x){
        int l = 0;
        int r = a.length - 1;
        while (l <= r){
            int mid = l + (r-l)/2;
            if (a[mid]==x)
                return 1;
            else if (a[mid] < x)
                l = mid+1;
            else
                r = mid-1;
        }
        return -1;
    }

    public static int upperBound(long[] arr,long key){
        int start=0;int end=arr.length-1;
        int idx=-1;
        int mid;
        while(start<=end){
            int i=(start+end)/2;
            if(arr[i]<key){
                start=i+1;
            }
            else if(arr[i]>key){
                end=i-1;
            }
            else{
                idx=i;
                start=i+1;
            }
        }

        return idx;    }

    public static int lowerBound(long[] arr,long key){
        int start=0;int end=arr.length-1;
        int idx=-1;
        int mid;
        while(start<=end){
            int i=(start+end)/2;
            if(arr[i]<key){
                start=i+1;
            }
            else if(arr[i]>key){
                end=i-1;
            }
            else{
                idx=i;
                end=i-1;
            }
        }
        return idx;
    }

    public static int searchInsert(long[] nums, long target) {
        int s=0,e=nums.length-1;
        int mid;
        if(target<nums[0]){
            return 0;
        }
        while(s<=e){
            mid=(s+e)/2;
            if(nums[mid]>target){
                e=mid-1;
            }
            else if(nums[mid]==target){
                return mid;
            }
            else{
                s=mid+1;
            }
        }
        return s;
    }

    static boolean isPrime(long n) {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;

        if (n % 2 == 0 || n % 3 == 0)
            return false;

        for (long i = 5; i <= Math.sqrt(n) + 1; i += 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;

        return true;
    }

    public static long fastExpo(long a,int n,int mod){
        if (n == 0)
            return 1;
        else{
            if ((n&1) == 1){
                long x = fastExpo(a,n/2,mod);
                return (((a*x)%mod)*x)%mod;
            }
            else{
                long x = fastExpo(a,n/2,mod);
                return (((x%mod)*(x%mod))%mod)%mod;
            }
        }
    }

    public static long modInverse(long n,int p){
        return fastExpo(n,p-2,p);
    }

    public static long nCr(int n,int r,long[] fact,int mod){
        long val =  (((fact[n] * modInverse(fact[r],mod))%mod)*modInverse(fact[n-r],mod))%mod;
        return val;
    }

    public static void factorial(long[] fact,int n,int mod){
        for (int i=1;i<=n;i++){
            fact[i] = (fact[i-1] * i)%mod;
        }
    }

    public static int log2(long val){
        return (int) Math.floor(Math.log(val)/Math.log(2));
    }

    public static boolean isSubSequence(String s,String t){
        int i = 0;
        int j = 0;
        while (i < s.length() && j < t.length()){
            if (s.charAt(i) == t.charAt(j))
                j++;
            i++;
        }
        return j == t.length();
    }

    public static ArrayList<Long> getAllFactors(long x){
        ArrayList<Long> ans = new ArrayList<>();
        for (long i = 1; i <= Math.sqrt(x); i++) {
            if (x%i == 0){
                if (x/i == i){
                    ans.add(i);
                }
                else{
                    ans.add(i);
                    ans.add(x/i);
                }
            }
        }
        return ans;
    }

    public static boolean isPerfectSquare(long x){
        double val = Math.sqrt(x);
        return val*val == (double)x;
    }

    public static ArrayList<Integer> buildSieve(int n){
        boolean[] sieve = new boolean[n+1];
        Arrays.fill(sieve,true);
        sieve[0] = sieve[1] = false;
        for (int i = 2; i <= Math.sqrt(n+1) ; i++) {
            if (sieve[i]){
                for (int j = 2*i; j < n+1; j += i) {
                    sieve[j] = false;
                }
            }
        }
        ArrayList<Integer> primes = new ArrayList<>();
        for (int i = 0; i < sieve.length; i++) {
            if (sieve[i]){
                primes.add(i);
            }
        }
        return primes;
    }

    public static int getLowBit(int n){
        int x = 0;
        while ((n&1) != 1){
            x++;
            n >>= 1;
        }
        return 1 << x;
    }

    public static void solve() throws IOException {
        char s = sc.next().charAt(0);
        char e = sc.next().charAt(0);
        long n = sc.nextLong();
        n = n%4;
        if (n == 0 || n == 2){
            System.out.println("undefined");
            return;
        }
        if (n == 1){
            if (s == '^'){
                if (e == '>'){
                    System.out.println("cw");
                }
                else if (e == '<'){
                    System.out.println("ccw");
                }
                else
                    System.out.println("undefined");
                return;
            }
            if (s == '>'){
                if (e == 'v'){
                    System.out.println("cw");
                }
                else if (e == '^'){
                    System.out.println("ccw");
                }
                else
                    System.out.println("undefined");
                return;
            }
            if (s == 'v'){
                if (e == '<'){
                    System.out.println("cw");
                }
                else if (e == '>'){
                    System.out.println("ccw");
                }
                else
                    System.out.println("undefined");
                return;
            }
            if (s == '<'){
                if (e == '^'){
                    System.out.println("cw");
                }
                else if (e == 'v'){
                    System.out.println("ccw");
                }
                else
                    System.out.println("undefined");
                return;
            }
        }

        if (n == 3){
            if (s == '^'){
                if (e == '>'){
                    System.out.println("ccw");
                }
                else if (e == '<'){
                    System.out.println("cw");
                }
                else
                    System.out.println("undefined");
                return;
            }
            if (s == '>'){
                if (e == 'v'){
                    System.out.println("ccw");
                }
                else if (e == '^'){
                    System.out.println("cw");
                }
                else
                    System.out.println("undefined");
                return;
            }
            if (s == 'v'){
                if (e == '<'){
                    System.out.println("ccw");
                }
                else if (e == '>'){
                    System.out.println("cw");
                }
                else
                    System.out.println("undefined");
                return;
            }
            if (s == '<'){
                if (e == '^'){
                    System.out.println("ccw");
                }
                else if (e == 'v'){
                    System.out.println("cw");
                }
                else
                    System.out.println("undefined");
                return;
            }
        }
    }
    public static void main(String[] args) throws IOException {
        int t;
//        t = sc.nextInt();
        t = 1;
        while (t-- > 0){
            solve();
        }
        System.gc();
    }
}