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 java.io.*;
	import java.math.BigInteger;
	import java.util.*;
	
	import javax.sound.midi.Synthesizer;
	
	
	public class Main
	{
		private InputStream is;
		private PrintWriter out;
		int time = 0, freq[], start[], end[], dist[], black[], MOD = (int) (1e9 + 7), arr[], weight[][], x[], y[], parent[];
		int MAX = 1000001, N, K;
		long red[], ans = Long.MAX_VALUE;
	
		ArrayList<Integer>[] amp;
		ArrayList<Pair>[] pmp;
		boolean b[];
		boolean boo[][], b1[];
		Pair prr[];
		HashMap<Pair, Integer> hm = new HashMap();
		int Dp[][] = new int[1100][1100];
	
		void soln() 
		{
			is = System.in;
			out = new PrintWriter(System.out);
			long s = System.currentTimeMillis();
			solve();
	
			// out.close();
			out.flush();
			// tr(System.currentTimeMillis() - s + "ms");
		}
	
		static class ST1 // min ST
		{
			long arr[], st[];
			int size;
	
			ST1(long a[]) {
				arr = a.clone();
				size = 10 * arr.length;
				st = new long[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]);
			}
	
			void update(int ss, int se, int idx, long val, int si) {
				if (ss == se) {
					// if(si==idx+1)
					st[si] = val;
					return;
				}
				int mid = (ss + se) / 2;
				if (ss <= idx && idx <= mid) {
					update(ss, mid, idx, val, 2 * si);
				} else {
					update(mid + 1, se, idx, val, 2 * si + 1);
				}
				int v = 2 * si;
				st[si] = Math.min(st[v], st[v + 1]);
			}
	
			long get(int ss, int se, int l, int r, int si) {
				if (l > se || r < ss || l > r)
					return Long.MAX_VALUE / 1000;
				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));
			}
		}
	
		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 D[][];
		char ch[][], ch1[];
		int hash = 29;
		int x2, y2;
		HashSet<Integer>[] hs = (HashSet<Integer>[]) new HashSet[110];
		cell[] c;
		 boolean ar[] = new boolean[1000];
		Pair[] p = new Pair[4];
		 int a1[] = new int[7];
		 int a2[] = new int[7];
		 int a3[] = new int[7];
		 int a4[] = new int[7];
		 void solve()
		 {
			int n = ni(),  x = ni();
			TreeSet<String> ts = new TreeSet<>();
			for(int i = 0; i< n; i++) {
				String s[] = new String[4];
				for(int j = 0; j < 4; j++) {
					s[j] = ns();
					int cnt = 0;
					for(int k = s[j].length()-1; k >= 0; k--) {
						if(isVowel(s[j].charAt(k))) cnt++;
						if(cnt == x) {
							s[j] = s[j].substring(k, s[j].length());
							break;
						}
					}
					if(cnt<x) {
						System.out.println("NO");
						return;
					}
				}
				ts.add(check(s));
			}
			if(ts.size()==1) {
				if(ts.contains("aaaa") || ts.contains("abab") || ts.contains("abba") || ts.contains("aabb"))
				System.out.println(ts.pollFirst());
				else System.out.println("NO");
			}
			else if(ts.size()==2) {
				if(ts.pollFirst().equals("aaaa")) {
					if(ts.contains("aaaa") || ts.contains("abab") || ts.contains("abba") || ts.contains("aabb"))
					System.out.println(ts.pollFirst());
					else System.out.println("NO");
				}
				else System.out.println("NO");
			}
			else {
				System.out.println("NO");
			}
		 }
		 String check(String[] s) {
			 char ch[] = new char[] {'a','a','a','a'};
			 boolean b = false;
			 for(int i = 0;i<4;i++) {
				 if(i>0) {
					 if(ch[i]=='a') continue;
				 }
				 for(int j = i+1;j<4;j++) {
					 if(!s[i].equals(s[j])) {
						 if(ch[i] == 'a' && ch[j]=='a') ch[j] = 'b';
						 else if(ch[j]=='a') continue;
						 else {
							 System.out.println("NO");
							 System.exit(0);
						 }
					 }
					 else b = true;
				 }
			 }
			 return new String(ch);
		 }
		 boolean isVowel(char c) {
			 if(c=='a' || c=='e' ||c=='i' ||c=='o' ||c=='u' ) return true;
					 return false;
		 }
		 void recur1(int[] a1, int[] a2) {
			 for(int i = 1; i< 7;i++) {
				 for(int j = 1; j< 7;j++) {
					 ar[a1[i]*10+a2[j]] = true;
					 ar[a2[j]*10+a1[i]] = true;
				 }
			 }
		 }
		 int dfs(int x) {
			 b[x] = true;
			 for(int i : amp[x]) {
				 if(!b[i]) {
					 dist[i] = dist[x]+1;
					 arr[x] += dfs(i);
				 }
			 }
			 return ++arr[x];
		 }
		boolean binaryS(int a, int b, int c, int d) {
			double l = 0, r = 90;
			for(int count = 0;count<=300;count++)
			{
				double mid = (l + r) / 2;
				double temp = mid * Math.PI / 180;
				double x1 = Math.cos(temp) * c;
				double x2 = Math.sin(temp) * c;
				temp = Math.PI / 2 - temp;
				double y1 = Math.cos(temp) * d;
				double y2 = Math.sin(temp) * d;
				if ((x1 + y1 <= a) && (x2 + y2 <= b)) return true;
				else if (x1 + y1 > a) l = mid;
				else r = mid;
			}
			return false;
		}
		void bfs(int s, int n) {
			b = new boolean[n];
			dist = new int[n];
			Arrays.fill(dist, 1000000);
			dist[s] = 0;
			b[s] = true;
			Queue<Integer> q = new LinkedList<>();
			q.add(s);
			while(!q.isEmpty()) {
				int y = q.poll();
				for(int i : amp[y]) {
					dist[i] = min(dist[i],dist[y]+1);
					if(!b[i]) {
						b[i] = true;
						q.add(i);
					}
				}
			}
		}
		boolean check(String s, String s1) {
			char ch1[] = s.toCharArray(), ch2[] = s1.toCharArray();
			int arr[] = new int[10];
			for(char c : ch1) {
				arr[c-'0']++;
			}
			int ans = 0;
			for(char c:ch2) {
				arr[c-'0']--;
			}
			
			for(int i:arr) ans += ((i>0)?i:0);
			return ans==3;
		}
		void seive(int n)
		{
			start = new int[n];
			for(int i = 2;i<n;i++) {
				if(start[i]==0) {
					for(int j = 2*i;j<n;j+=i) {
						start[j] = i;
					}
				}
			}
		}
		void print(int[][] arr) 
		{
			int seed = 110, n = arr.length - 220;
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < n; j++) {
					System.out.print(arr[i + seed][j + seed] + " ");
				}
				System.out.println();
			}
			System.out.println();
		}
	
		 class cell implements Comparable<cell>
		 {
			int s, d, p, i;
	
			cell(int t, int d, int p, int i) {
				this.s = t;
				this.p = p;
				this.d = d;
				this.i = i;
			}
	
			public int compareTo(cell other) {
				// return Integer.compare(val, other.val);
				return Long.compare(d, other.d) != 0 ? (Long.compare(d, other.d)): (Long.compare(i,other.i));
												// other.v));//((Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)):
												// (Long.compare(v, other.v)))
				// &(Long.compare(u, other.v) != 0 ? (Long.compare(u, other.v)):
				// (Long.compare(v, other.u))));
			}
	
			public String toString() {
				return this.d + " " + this.s +" "+this.p+" "+this.i;
			}
		}
	
		int abs(int x)
		{
			return ((x > 0) ? x : -x);
		}
	
		long ret(int p) 
		{
			if (p >= 0)
				return 0;
			else
				return 1;
		}
	
		long val(int p, int a, int b) 
		{
			if (p >= 0) {
				return (a * 1l * p);
			}
			return (b * 1l * p);
		}
	
		void ternary_search(int l, int r) 
		{
			// System.out.println(l+" "+r+" "+ans);
			// for(int i : arr) System.out.print(i+" ");
			// System.out.println();
			if (r >= l) {
				int mid1 = l + (r - l) / 3;
				int mid2 = r - (r - l) / 3;
				long cnt1 = 0, cnt2 = 0;
				cnt1 = compute(mid1);
				cnt2 = compute(mid2);
				// System.out.println(mid1+" "+ cnt1+" "+mid2+" "+cnt2);
				ans = Math.min(cnt1, cnt2);
				if (cnt1 < cnt2) {
					ternary_search(l, mid2 - 1);
				} else {
					ternary_search(mid1 + 1, r);
				}
			}
			return;
		}
	
		long compute(int x) 
		{
			long ans = 0;
			int c = arr[0];
			for (int i = 1; i <= x; i++) {
				ans += max(c + 1 - arr[i], 0);
				c = max(c + 1, arr[i]);
			}
			int temp = arr[x];
			arr[x] = max(c + 1, arr[x]);
			// SSystem.out.println(arr[x]+" "+ans);
			c = arr[arr.length - 1];
			for (int i = arr.length - 1; i > x; i--) {
				ans += max(c + 1 - arr[i - 1], 0);
				c = max(c + 1, arr[i - 1]);
			}
			arr[x] = temp;
			return ans;
		}
	
		public int getParent(int x) 
		{
			while (parent[x] != x) {
				parent[x] = parent[parent[x]];
				x = parent[x];
			}
			return x;
		}
	
		void getFactors(int n, int x)
		{
			for (int i = 1; i * i <= n; i++) {
				if (n % i == 0) {
					hs[x].add(i);
					hs[x].add(n / i);
				}
			}
		}
	
		void recur(int a, int b, int k) 
		{
			if (k == 0) {
				if (a == x2 && b == y2)
					ans++;
				return;
			}
			recur(a, b + 1, k - 1);
			recur(a, b - 1, k - 1);
			recur(a + 1, b, k - 1);
			recur(a - 1, b, k - 1);
		}
	
		int min(int a, int b) 
		{
			return (a < b) ? a : b;
		}
	
		/*private class Cell implements Comparable<Cell> {
			int u, v, s;
	
			public Cell(int u, int v, int s) {
				this.u = u;
				this.v = v;
				this.s = s;
			}
	
			public int hashCode() {
				return Objects.hash();
			}
	
			public int compareTo(Cell other) {
				return (Long.compare(s, other.s) != 0 ? (Long.compare(s, other.s))
						: (Long.compare(v, other.v) != 0 ? Long.compare(v, other.v) : Long.compare(u, other.u)))
						& ((Long.compare(s, other.s) != 0 ? (Long.compare(s, other.s))
								: (Long.compare(u, other.v) != 0 ? Long.compare(u, other.v) : Long.compare(v, other.u))));
			}
	
			public String toString() {
				return this.u + " " + this.v;
			}
		}*/
	
		class Pair implements Comparable<Pair>
		{
			int u ,v,i;
	
			Pair(int u, int v) {
				this.u = u;
				this.i = v;
			}
	
			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(i, other.i));// ((Long.compare(u,
			
			}									
			public String toString() {
				return this.u + " " + this.v +" "+this.i;
			}
		}
	
		int max(int a, int b) 
		{
			if (a > b)
				return a;
			return b;
		}
	
		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(), y1 = ni();
				amp[x1-1].add(y1-1);
				amp[y1-1].add(x1-1);
			}
		}
		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 long gcd(long a, long b)
		{
			if (b == 0)
				return a;
			return gcd(b, a % b);
		}
	
		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));
		}
	}