Problem: There always is something to choose from! And now, instead of "Noughts and Crosses", Inna choose a very unusual upgrade of this game. The rules of the game are given below:

There is one person playing the game. Before the beginning of the game he puts 12 cards in a row on the table. Each card contains a character: "X" or "O". Then the player chooses two positive integers a and b (a·b = 12), after that he makes a table of size a × b from the cards he put on the table as follows: the first b cards form the first row of the table, the second b cards form the second row of the table and so on, the last b cards form the last (number a) row of the table. The player wins if some column of the table contain characters "X" on all cards. Otherwise, the player loses.

Inna has already put 12 cards on the table in a row. But unfortunately, she doesn't know what numbers a and b to choose. Help her win the game: print to her all the possible ways of numbers a, b that she can choose and win.

Input

The first line of the input contains integer t (1 ≤ t ≤ 100). This value shows the number of sets of test data in the input. Next follows the description of each of the t tests on a separate line.

The description of each test is a string consisting of 12 characters, each character is either "X", or "O". The i-th character of the string shows the character that is written on the i-th card from the start.

Output

For each test, print the answer to the test on a single line. The first number in the line must represent the number of distinct ways to choose the pair a, b. Next, print on this line the pairs in the format axb. Print the pairs in the order of increasing first parameter (a). Separate the pairs in the line by whitespaces.

Examples

Input

4
OXXXOXOOXOOX
OXOXOXOXOXOX
XXXXXXXXXXXX
OOOOOOOOOOOO


Output

3 1x12 2x6 4x3
4 1x12 2x6 3x4 6x2
6 1x12 2x6 3x4 4x3 6x2 12x1
0

Solution (in JAVA):

Solution:
///package CodeForce;
import java.io.*;
import java.util.*;
/**
 *
 * @author prabhat
 */
public class P400A {

	   static final int MAX1 = 1000000+10;
	   static final long mod = 1000000007;
	   static final long MOD = 100000000000000007L;
	   static int phiSum[] = new int[MAX1];
	   static int phi[] = new int[MAX1];
	   static long[] res=new long[MAX1];
	   static int a[];
	   static long BIT[];
	   static int n,m,k,p;
	   static boolean[] b;
	   static long[][] pascal;
           static long[][] dp;
           static LinkedList<Integer> list[];
           static ArrayList<Integer> l;
           static TreeSet<Integer> ts;
           static int max=1<<11;
           static char[] s;
	    public static void main(String[] args) throws IOException{
	       
	        InputReader in = new InputReader(System.in);
               //BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	        PrintWriter pw = new PrintWriter(System.out,true);
              int t=in.ii();
              while(t-->0)
              {
                s=in.next().trim().toCharArray();
               ts=new TreeSet<>();
                for(int i=1;i<=12;i++)
                {
                   if(12%i==0)
                   {
                      if(sol(i,12/i))
                          ts.add(i);
                   }
                }
                pw.print(ts.size()+" ");
                for(int o:ts)
                    pw.print(o+"x"+(12/o)+" ");
                pw.println();
              }
                
	      pw.close();
	    }
         static boolean sol(int a,int b)
            {
               boolean res=false;
               for(int c=0;c<b;c++)
               {
                  boolean f=true;
                  for(int r=0;r<a;r++)
                  {
                    f&=(s[r*b+c]=='X');
                  }
                  res|=f;
               }
            return res;
            }
            static void pascal()
	    {
	  	  pascal=new long[max][max];
	  	  for(int i=0;i<max;i++)
	  	  {
	  		  pascal[i][0]=1L;
	  		  for(int j=1;j<=i;j++)
	  		  {
	  			  pascal[i][j]=(int) ((pascal[i-1][j]+pascal[i-1][j-1])%mod);
	  		  }
	  	  }
	  	 
	    }
       public static long pow(long n,long p)
	{
		long  result = 1L;
		  if(p==0)
		    return 1L;
		if (p==1)
		    return n;
		while(p!=0)
		{
		    if(p%2==1)
		        result *= n;
		    p >>=1;
		    n*=n;
		}
		return result;
	 
	}
	 
	 
    boolean nextPermutation(int[] p) {
        for (int a = p.length - 2; a >= 0; --a)
        {
            if (p[a] < p[a + 1])
                for (int b = p.length - 1; ; --b)
                    if (p[b] > p[a]) {
                        int t = p[a];
                        p[a] = p[b];
                        p[b] = t;
                        for (++a, b = p.length - 1; a < b; ++a, --b) 
                        {
                            t = p[a];
                            p[a] = p[b];
                            p[b] = t;
                        }
                        return true;
                    }
        }
        return false;
     }

	    public static long nCr(long total, long choose)
		{
			if(total < choose)
				return 0;
			if(choose == 0 || choose == total)
				return 1;
			return nCr(total-1,choose-1)+nCr(total-1,choose);
		}
	    static void compute() {
	    		for (int i = 0; i < MAX1; i++) {
	    			phi[i] = 0;
	    		}
	          phi[1]=1;
	    		for (int i = 2; i < MAX1; i++) {
	    			if (phi[i] == 0) {
	    				phi[i] = i - 1;
	     
	    				for (int j = 2 * i; j < MAX1; j += i) {
	    					 if(phi[j]==0) phi[j] = j ;
	    					phi[j] -= (phi[j]/i);
	    				}
	    			}
	    		}
	     
	    		for (int i = 1; i < MAX1; i++) {
	    			for (int j = i, k = 1; j < MAX1; j += i,k++) {
	    				phiSum[j] += i * phi[k];
	    			}
	    		}
	    		//System.out.println(Arrays.toString(phiSum));
                /*botharrays  res and phisum gives the same arrays so please don't worry*/
	    		
	    		for(int i=1;i<MAX1;i++)
	    		{
	    			for(int j=i+i;j<MAX1;j+=i)
	    			{
	    			   res[j]=res[j]+1L*i*phi[j/i];
	    			}
	    		}
	    		for(int i=1;i<=1000000;i++)
	    			res[i]=res[i]+res[i-1];
	    	//System.out.println(Arrays.toString(res));
	    						
	    		
	    		
	    }
	    public static void Seive()
		{
			l=new ArrayList<>();
			 b=new boolean[80001];
			Arrays.fill(b, true);
			b[0]=false;
			b[1]=false;
			
			for(int i=2;i<=(80000);i++)
			{
				if(b[i])
				{
					l.add(i);
				 for(int j=i*2;j<=80000;j+=i)
					{
						     b[j]=false;
						
					}
				}
				
			}
			
		}
	  
	    private static class DSU{
			int[] parent;
			int[] rank;
			int cnt;
			public DSU(int n){
				parent=new int[n];
				rank=new int[n];
				for(int i=0;i<n;i++){
					parent[i]=i;
					rank[i]=1;
				}
				cnt=n;
			}
			int find(int i){
		        while(parent[i] !=i){
		        	parent[i]=parent[parent[i]];
		        	i=parent[i];
		        }
		        return i;
		    }
			int Union(int x, int y){
		        int xset = find(x);
		        int yset = find(y);
		        if(xset!=yset)
		        	cnt--;
		        if(rank[xset]<rank[yset]){
		        	parent[xset] = yset;
			        rank[yset]+=rank[xset];
			        rank[xset]=0;
			        return yset;
		        }else{
		        	parent[yset]=xset;
		        	rank[xset]+=rank[yset];
		        	rank[yset]=0;
		        	return xset;
		        }
		    }
		}
	  public static int[][] packU(int n, int[] from, int[] to, int max) {
		    
		    int[][] g = new int[n][];
		    int[] p = new int[n];
		    for (int i = 0; i < max; i++) p[from[i]]++;
		    for (int i = 0; i < max; i++) p[to[i]]++;
		    for (int i = 0; i < n; i++) g[i] = new int[p[i]];
		    for (int i = 0; i < max; i++) {
		        g[from[i]][--p[from[i]]] = to[i];
		        g[to[i]][--p[to[i]]] = from[i];
		    }
		    return g;
		}
		public static int[][] parents3(int[][] g, int root) {
		    int n = g.length;
		    int[] par = new int[n];
		    Arrays.fill(par, -1);
	 
		    int[] depth = new int[n];
		    depth[0] = 0;
	 
		    int[] q = new int[n];
		    q[0] = root;
		    for (int p = 0, r = 1; p < r; p++) {
		        int cur = q[p];
		        for (int nex : g[cur]) {
		            if (par[cur] != nex) {
		                q[r++] = nex;
		                par[nex] = cur;
		                depth[nex] = depth[cur] + 1;
		            }
		        }
		    }
		    return new int[][]{par, q, depth};
		}
		public static int lower_bound(int[] nums, int target) {
	        int low = 0, high = nums.length - 1;
	        while (low < high) {
	            int mid = low + (high - low) / 2;
	            if (nums[mid] < target)
	                low = mid + 1;
	            else
	                high = mid;
	        }
	        return nums[low] == target ? low : -1;
	    }
	 
	    public static int upper_bound(int[] nums, int target) {
	        int low = 0, high = nums.length - 1;
	        while (low < high) {
	            int mid = low + (high + 1 - low) / 2;
	            if (nums[mid] > target)
	                high = mid - 1;
	            else
	                low = mid;
	        }
	        return nums[low] == target ? low : -1;
	    }
	  public static boolean palin(String s)
		{
		   int i=0;
		   int j=s.length()-1;
		   while(i<j)
		   {
			   if(s.charAt(i)==s.charAt(j))
			   {
				   i++;
				   j--;
			   }
			   else return false;     
		   }
		   return true;
		}
		
	    static boolean CountPs(String s,int n)
	       {
	    	boolean b=false;
	    	     char[] S=s.toCharArray();
		       int[][] dp=new int[n][n];
		       boolean[][] p=new boolean[n][n];
		       for(int i=0;i<n;i++)p[i][i]=true;
		     
		       for(int i=0;i<n-1;i++)
		       {
		    	   if(S[i]==S[i+1])
		    	   {
		    		p[i][i+1]=true;
		    		dp[i][i+1]=1;
		    		b=true;
		    	   }
		       }
		    
		       for(int gap=2;gap<n;gap++)
		       {
		    	   for(int i=0;i<n-gap;i++)
		    	   {
		    		   int j=gap+i;
		    		   if(S[i]==S[j]&&p[i+1][j-1]){p[i][j]=true;}
		    		  
		    		  if(p[i][j])
		    			   dp[i][j]=dp[i][j-1]+dp[i+1][j]+1-dp[i+1][j-1];
		    		   
		    		   else  dp[i][j]=dp[i][j-1]+dp[i+1][j]-dp[i+1][j-1];
		    		  
		    		   if(dp[i][j]>=1){b=true;}
		    	   }
		       }
		      
		    return b; 
	   // return dp[0][n-1];
		       
	    }
	  
	  
	  
	 
	 
	public static int gcd(int a,int b)
	{
		int res=1;
		while(a>0)
		{
			res=a;
			a=b%a;
			b=res;
		}
		return res;
	}
	 
	 
	public static long pow(long n,long p,long m)
	{
		 long  result = 1;
		  if(p==0)
		    return 1;
		if (p==1)
		    return n;
		while(p!=0)
		{
		    if(p%2==1)
		        result *= n;
		    if(result>=m)
		    result%=m;
		    p >>=1;
		    n*=n;
		    if(n>=m)
		    n%=m;
		}
		return result;
	}
	
	 
	 
	static class Edge implements Comparator<Edge> {
		private int u;
		private int v;
		private int w;
		public Edge() {
		}
		public Edge(int u, int v, int w) {
			this.u=u;
			this.v=v;
			this.w=w;
		}
		public int getU() {
			return u;
		}
		public void setU(int u) {
			this.u = u;
		}
		public int getV() {
			return v;
		}
		public void setV(int v) {
			this.v = v;
		}
		public int getW() {
			return w;
		}
		public void setW(int w) {
			this.w = w;
		      }
		public int compareTo(Edge e)
		  {
			return this.getW() - e.getW();
		}
		@Override
		public String toString() {
			return "Edge [u=" + u + ", v=" + v + ", w=" + w + "]";
		}
		@Override
		public int compare(Edge arg0, Edge arg1) {
			// TODO Auto-generated method stub
			return 0;
		}
	}
	 
	 
	 
	static class Pair implements Comparable<Pair>
	{
		int a,b;
		Pair (int a,int b)
		{
			this.a=a;
			this.b=b;
		}
	 
		public int compareTo(Pair o) {
			// TODO Auto-generated method stub
			if(this.a!=o.a)
			return -Integer.compare(this.a,o.a);
			else
				return -Integer.compare(this.b, o.b);
			//return 0;
		}
		public boolean equals(Object o) {
	       if (o instanceof Pair) {
	           Pair p = (Pair)o;
	           return p.a == a && p.b == b;
	       }
	       return false;
	   }
	   public int hashCode() {
	       return new Integer(a).hashCode() * 31 + new Integer(b).hashCode();
	   }
	}
	 
		static class InputReader
		{
			private InputStream stream;
			private byte[] buf = new byte[1024];
			private int curChar;
			private int numChars;
			private SpaceCharFilter filter;
			
			public InputReader(InputStream stream)
			{
				this.stream = stream;
			}
			
			public int read()
			{
				if (numChars==-1) 
					throw new InputMismatchException();
				
				if (curChar >= numChars)
				{
					curChar = 0;
					try 
					{
						numChars = stream.read(buf);
					}
					catch (IOException e)
					{
						throw new InputMismatchException();
					}
					
					if(numChars <= 0)				
						return -1;
				}
				return buf[curChar++];
			}
		 
			public String nextLine()
			{
				BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
				String str = "";
	            try
	            {
	                str = br.readLine();
	            }
	            catch (IOException e)
	            {
	                e.printStackTrace();
	            }
	            return str;
			}
			public int ii()
			{
				int c = read();
				
				while(isSpaceChar(c)) 
					c = read();
				
				int sgn = 1;
				
				if (c == '-') 
				{
					sgn = -1;
					c = read();
				}
				
				int res = 0;
				do 
				{
					if(c<'0'||c>'9') 
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = read();
				}
				while (!isSpaceChar(c)); 
				
				return res * sgn;
			}
			
			public long il() 
			{
				int c = read();
				while (isSpaceChar(c))
					c = read();
				int sgn = 1;
				if (c == '-') 
				{
					sgn = -1;
					c = read();
				}
				long res = 0;
				
				do 
				{
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = read();
				}
				while (!isSpaceChar(c));
					return res * sgn;
			}
			
			public double nextDouble() 
			{
				int c = read();
				while (isSpaceChar(c))
					c = read();
				int sgn = 1;
				if (c == '-') 
				{
					sgn = -1;
					c = read();
				}
				double res = 0;
				while (!isSpaceChar(c) && c != '.') 
				{
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, ii());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = read();
				}
				if (c == '.') 
				{
					c = read();
					double m = 1;
					while (!isSpaceChar(c)) 
					{
						if (c == 'e' || c == 'E')
							return res * Math.pow(10, ii());
						if (c < '0' || c > '9')
							throw new InputMismatchException();
						m /= 10;
						res += (c - '0') * m;
						c = read();
					}
				}
				return res * sgn;
			}
			
			public String readString() 
			{
				int c = read();
				while (isSpaceChar(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do 
				{
					res.appendCodePoint(c);
					c = read();
				} 
				while (!isSpaceChar(c));
				
				return res.toString();
			}
		 
			public boolean isSpaceChar(int c) 
			{
				if (filter != null)
					return filter.isSpaceChar(c);
				return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			}
		 
			public String next() 
			{
				return readString();
			}
			
			public interface SpaceCharFilter 
			{
				public boolean isSpaceChar(int ch);
			}
		}
	}