Vera adores poems. All the poems Vera knows are divided into quatrains (groups of four lines) and in each quatrain some lines contain rhymes.

Let's consider that all lines in the poems consist of lowercase Latin letters (without spaces). Letters "a", "e", "i", "o", "u" are considered vowels.

Two lines rhyme if their suffixes that start from the k-th vowels (counting from the end) match. If a line has less than k vowels, then such line can't rhyme with any other line. For example, if k = 1, lines commit and hermit rhyme (the corresponding suffixes equal it), and if k = 2, they do not rhyme (ommit ≠ ermit).

Today on a literature lesson Vera learned that quatrains can contain four different schemes of rhymes, namely the following ones (the same letters stand for rhyming lines): 

  * Clerihew (aabb); 
  * Alternating (abab); 
  * Enclosed (abba). 



If all lines of a quatrain pairwise rhyme, then the quatrain can belong to any rhyme scheme (this situation is represented by aaaa).

If all quatrains of a poem belong to the same rhyme scheme, then we can assume that the whole poem belongs to this rhyme scheme. If in each quatrain all lines pairwise rhyme, then the rhyme scheme of the poem is aaaa. Let us note that it doesn't matter whether lines from different quatrains rhyme with each other or not. In other words, it is possible that different quatrains aren't connected by a rhyme.

Vera got a long poem as a home task. The girl has to analyse it and find the poem rhyme scheme. Help Vera cope with the task.

Input

The first line contains two integers n and k (1 ≤ n ≤ 2500, 1 ≤ k ≤ 5) — the number of quatrains in the poem and the vowel's number, correspondingly. Next 4n lines contain the poem. Each line is not empty and only consists of small Latin letters. The total length of the lines does not exceed 104.

If we assume that the lines are numbered starting from 1, then the first quatrain contains lines number 1, 2, 3, 4; the second one contains lines number 5, 6, 7, 8; and so on.

Output

Print the rhyme scheme of the poem as "aabb", "abab", "abba", "aaaa"; or "NO" if the poem does not belong to any of the above mentioned schemes.

Examples

Input

1 1
day
may
sun
fun


Output

aabb


Input

1 1
day
may
gray
way


Output

aaaa


Input

2 1
a
a
a
a
a
a
e
e


Output

aabb


Input

2 1
day
may
sun
fun
test
hill
fest
thrill


Output

NO

Note

In the last sample both quatrains have rhymes but finding the common scheme is impossible, so the answer is "NO".
import static java.lang.Math.*;
import java.util.*;
import java.io.*;

public class C {

    public void solve() throws Exception {

        int n = nextInt(), kk = nextInt();
        boolean aabb=true, abab=true, abba=true;
        for (int i=0; i<n; ++i) {
            String[] q = new String[4];
            int[] cnt = new int[4];
            for (int j=0; j<4; ++j) {
                q[j] = nextLine();
                int wcnt = 0;
                for (int k=q[j].length()-1; k>=0; --k) {
                    if (charIn(q[j].charAt(k), "aeiou")) wcnt++;
                    if (wcnt==kk) {
                        cnt[j] = q[j].length()-k;
                        break;
                    }
                }
                if (cnt[j]==0) halt("NO");
            }

            aabb &= fits(q, cnt, 0, 1, 2, 3);
            abba &= fits(q, cnt, 0, 3, 1, 2);
            abab &= fits(q, cnt, 0, 2, 1, 3);
        }

        int cnt = 0;
        cnt = (abab ? 1:0) + (abba ? 1:0) + (aabb ? 1:0);
        if (cnt>1) halt("aaaa");
        if (cnt==0) halt("NO");
        if (abab) halt("abab");
        if (abba) halt("abba");
        halt("aabb");


    }

    boolean fits(String[] q, int[] cnt, int a1, int a2, int b1, int b2) {
        if (cnt[a1]!=cnt[a2] || cnt[b1]!=cnt[b2]) return false;
        for (int i=0; i<cnt[a1]; ++i)
            if (q[a1].charAt(q[a1].length()-i-1) != q[a2].charAt(q[a2].length()-i-1))
                return false;
        for (int i=0; i<cnt[b1]; ++i)
            if (q[b1].charAt(q[b1].length()-i-1) != q[b2].charAt(q[b2].length()-i-1))
                return false;
        return true;
    }

    boolean charIn(char ch, String s) {
        if (s==null) return false;
        for (int i=0; i<s.length(); ++i) if (ch==s.charAt(i)) return true;
        return false;
    }

    ////////////////////////////////////////////////////////////////////////////

    boolean showDebug = true;
    static boolean useFiles = false;
    static String inFile = "input.txt";
    static String outFile = "output.txt";

    double EPS = 1e-7;
    int INF = Integer.MAX_VALUE;
    long INFL = Long.MAX_VALUE;
    double INFD = Double.MAX_VALUE;


    int absPos(int num) {
        return num<0 ? 0:num;
    }
    long absPos(long num) {
        return num<0 ? 0:num;
    }
    double absPos(double num) {
        return num<0 ? 0:num;
    }

    int min(int... nums) {
        int r = INF;
        for (int i: nums)
            if (i<r) r=i;
        return r;
    }
    int max(int... nums) {
        int r = -INF;
        for (int i: nums)
            if (i>r) r=i;
        return r;
    }
    long minL(long... nums) {
        long r = INFL;
        for (long i: nums)
            if (i<r) r=i;
        return r;
    }
    long maxL(long... nums) {
        long r = -INFL;
        for (long i: nums)
            if (i>r) r=i;
        return r;
    }
    double minD(double... nums) {
        double r = INFD;
        for (double i: nums)
            if (i<r) r=i;
        return r;
    }
    double maxD(double... nums) {
        double r = -INFD;
        for (double i: nums)
            if (i>r) r=i;
        return r;
    }

    long sumArr(int[] arr) {
        long res = 0;
        for (int i: arr)
            res+=i;
        return res;
    }
    long sumArr(long[] arr) {
        long res = 0;
        for (long i: arr)
            res+=i;
        return res;
    }
    double sumArr(double[] arr) {
        double res = 0;
        for (double i: arr)
            res+=i;
        return res;
    }

    long partsFitCnt(long partSize, long wholeSize) {
        return (partSize+wholeSize-1)/partSize;
    }

    boolean odd(long num) {
        return (num&1)==1;
    }

    boolean hasBit(int num, int pos) {
        return (num&(1<<pos))>0;
    }

    long binpow(long a, int n) {
        long r = 1;
        while (n>0) {
            if ((n&1)!=0) r*=a;
            a*=a;
            n>>=1;
        }
        return r;
    }

    boolean isLetter(char c) {
        return (c>='a' && c<='z') || (c>='A' && c<='Z');
    }
    boolean isLowercase(char c) {
        return (c>='a' && c<='z');
    }
    boolean isUppercase(char c) {
        return (c>='A' && c<='Z');
    }
    boolean isDigit(char c) {
        return (c>='0' && c<='9');
    }

    String stringn(String s, int n) {
        if (n<1) return "";
        StringBuilder sb = new StringBuilder(s.length()*n);
        for (int i=0; i<n; ++i) sb.append(s);
        return sb.toString();
    }
    String str(Object o) {
        return o.toString();
    }


    long timer = System.currentTimeMillis();
    void startTimer() {
        timer = System.currentTimeMillis();
    }
    void stopTimer() {
        System.err.println("time: "+(System.currentTimeMillis()-timer)/1000.0);
    }


    static class InputReader {
        private byte[] buf;
        private int bufPos = 0, bufLim = -1;
        private InputStream stream;
        public InputReader(InputStream stream, int size) {
            buf = new byte[size];
            this.stream = stream;
        }
        private void fillBuf() throws IOException {
            bufLim = stream.read(buf);
            bufPos = 0;
        }
        char read() throws IOException {
            if (bufPos>=bufLim) fillBuf(); 
            return (char)buf[bufPos++];
        }
        boolean hasInput() throws IOException {
            if (bufPos>=bufLim) fillBuf();
            return bufPos<bufLim;
        }
    }

    static InputReader inputReader;
    static BufferedWriter outputWriter;

    char nextChar() throws IOException {
        return inputReader.read();
    }
    char nextNonWhitespaceChar() throws IOException {
        char c = inputReader.read();
        while (c<=' ') c=inputReader.read();
        return c;
    }
    String nextWord() throws IOException {
        StringBuilder sb = new StringBuilder();
        char c = inputReader.read();
        while (c<=' ') c=inputReader.read();
        while (c>' ') {
            sb.append(c);
            c = inputReader.read();
        }
        return new String(sb);
    }
    String nextLine() throws IOException {
        StringBuilder sb = new StringBuilder();
        char c = inputReader.read();
        while (c<=' ') c=inputReader.read();
        while (c!='\n' && c!='\r') {
            sb.append(c);
            c = inputReader.read();
        }
        return new String(sb);
    }
    int nextInt() throws IOException {
        int r = 0;
        char c = nextNonWhitespaceChar();
        boolean neg = false;
        if (c=='-') neg=true;
        else r=c-48;
        c = nextChar();
        while (c>='0' && c<='9') {
            r*=10;
            r+=c-48;
            c=nextChar();
        }
        return neg ? -r:r;
    }
    long nextLong() throws IOException {
        long r = 0;
        char c = nextNonWhitespaceChar();
        boolean neg = false;
        if (c=='-') neg=true;
        else r = c-48;
        c = nextChar();
        while (c>='0' && c<='9') {
            r*=10L;
            r+=c-48L;
            c=nextChar();
        }
        return neg ? -r:r;
    }
    double nextDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(nextWord());
    }
    int[] nextArr(int size) throws NumberFormatException, IOException {
        int[] arr = new int[size];
        for (int i=0; i<size; ++i)
            arr[i] = nextInt();
        return arr;
    }
    long[] nextArrL(int size) throws NumberFormatException, IOException {
        long[] arr = new long[size];
        for (int i=0; i<size; ++i)
            arr[i] = nextLong();
        return arr;
    }
    double[] nextArrD(int size) throws NumberFormatException, IOException {
        double[] arr = new double[size];
        for (int i=0; i<size; ++i)
            arr[i] = nextDouble();
        return arr;
    }
    String[] nextArrS(int size) throws NumberFormatException, IOException {
        String[] arr = new String[size];
        for (int i=0; i<size; ++i)
            arr[i] = nextWord();
        return arr;
    }
    char[] nextArrCh(int size) throws IOException {
        char[] arr = new char[size];
        for (int i=0; i<size; ++i)
            arr[i] = nextNonWhitespaceChar();
        return arr;
    }
    char[][] nextArrCh(int rows, int columns) throws IOException {
        char[][] arr = new char[rows][columns];
        for (int i=0; i<rows; ++i)
            for (int j=0; j<columns; ++j)
                arr[i][j] = nextNonWhitespaceChar();
        return arr;
    }
    char[][] nextArrChBorders(int rows, int columns, char border) throws IOException {
        char[][] arr = new char[rows+2][columns+2];
        for (int i=1; i<=rows; ++i)
            for (int j=1; j<=columns; ++j)
                arr[i][j] = nextNonWhitespaceChar();
        for (int i=0; i<columns+2; ++i) {
            arr[0][i] = border;
            arr[rows+1][i] = border;
        }
        for (int i=0; i<rows+2; ++i) {
            arr[i][0] = border;
            arr[i][columns+1] = border;
        }
        return arr;
    }

    void printf(String format, Object... args) throws IOException {
        outputWriter.write(String.format(format, args));
    }
    void print(Object o) throws IOException {
        outputWriter.write(o.toString());
    }
    void println(Object o) throws IOException {
        outputWriter.write(o.toString());
        outputWriter.newLine();
    }
    void print(Object... o) throws IOException {
        for (int i=0; i<o.length; ++i) {
            if (i!=0) outputWriter.write(' ');
            outputWriter.write(o[i].toString());
        }
    }
    void println(Object... o) throws IOException {
        print(o);
        outputWriter.newLine();
    }
    void printn(Object o, int n) throws IOException {
        String s = o.toString();
        for (int i=0; i<n; ++i) {
            outputWriter.write(s);
            if (i!=n-1) outputWriter.write(' ');
        }
    }
    void printnln(Object o, int n) throws IOException {
        printn(o, n);
        outputWriter.newLine();
    }
    void printArr(int[] arr) throws IOException {
        for (int i=0; i<arr.length; ++i) {
            if (i!=0) outputWriter.write(' ');
            outputWriter.write(Integer.toString(arr[i]));
        }
    }
    void printArr(long[] arr) throws IOException {
        for (int i=0; i<arr.length; ++i) {
            if (i!=0) outputWriter.write(' ');
            outputWriter.write(Long.toString(arr[i]));
        }
    }
    void printArr(double[] arr) throws IOException {
        for (int i=0; i<arr.length; ++i) {
            if (i!=0) outputWriter.write(' ');
            outputWriter.write(Double.toString(arr[i]));
        }
    }
    void printArr(String[] arr) throws IOException {
        for (int i=0; i<arr.length; ++i) {
            if (i!=0) outputWriter.write(' ');
            outputWriter.write(arr[i]);
        }
    }
    void printArr(char[] arr) throws IOException {
        for (char c: arr) outputWriter.write(c);
    }
    void printlnArr(int[] arr) throws IOException {
        printArr(arr);
        outputWriter.newLine();
    }
    void printlnArr(long[] arr) throws IOException {
        printArr(arr);
        outputWriter.newLine();
    }
    void printlnArr(double[] arr) throws IOException {
        printArr(arr);
        outputWriter.newLine();
    }
    void printlnArr(String[] arr) throws IOException {
        printArr(arr);
        outputWriter.newLine();
    }
    void printlnArr(char[] arr) throws IOException {
        printArr(arr);
        outputWriter.newLine();
    }
    void halt(Object... o) throws IOException {
        if (o.length!=0) println(o);
        outputWriter.flush(); outputWriter.close();
        System.exit(0);
    }

    void debug(Object... o) {
        if (showDebug) System.err.println(Arrays.deepToString(o));
    }


    public static void main(String[] args) throws Exception {
        Locale.setDefault(Locale.US);
        if (!useFiles) {
            inputReader = new InputReader(System.in, 1<<16);
            outputWriter = new BufferedWriter(new OutputStreamWriter(System.out), 1<<16);
        } else {
            inputReader = new InputReader(new FileInputStream(new File(inFile)), 1<<16);
            outputWriter = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(new File(outFile))), 1<<16);
        }
        new C().solve();
        outputWriter.flush(); outputWriter.close();
    }
}
