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:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.StringTokenizer;
import java.util.Vector;

public class Main {
	
	public static boolean debug = false;
	public static Reader in = new Reader();
	public static Writer out = new Writer();

	public static void main(String[] args) {
		int t = in.readInt();
		
		char[] cards;
		
		Vector<int[]> ans = new Vector<int[]>();
		
		while(t-->0) {
			cards = in.readLine().toCharArray();
			ans.clear();
			for(int a=1; a<=12; a++) {
				if(12%a==0 && wins(cards, a, 12/a)) {
					ans.add(new int[]{a, 12/a});
				}
			}
			out.print(ans.size());
			for(int[] a: ans) {
				out.printf(" %dx%d", a[0], a[1]);
			}
			out.println();
		}
		
		
		
		out.close();
	}
	
	public static boolean wins(char[] cards, int a, int b) {
		//out.println();
		//out.printfln("a: %d, b: %d", a, b);
		for(int j=0; j<b; j++) {
			int i;
			
			for(i=0; i<a; i++) {
				//out.printfln("i: %d, j: %d, c: %c", i, j, cards[i*b+j]);
				if(cards[i*b+j]=='O') {
					break;
				}
			}
			//out.println(j);
			if(i==a) {
				return true;
			}
		}
		return false;
	}
}

class Reader {
	private BufferedReader input;
	private StringTokenizer line = new StringTokenizer("");
	
	public Reader() {
		input = new BufferedReader(new InputStreamReader(System.in));
	}

	public Reader(String s) {
		try {
			input = new BufferedReader(new FileReader(s));
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}
	
	public void fill() {
		try {
			if(!line.hasMoreTokens()) line = new StringTokenizer(input.readLine());
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}
	
	public double nextDouble() {
		fill();
		return Double.parseDouble(line.nextToken());
	}
	
	public String nextWord() {
		fill();
		return line.nextToken();
	}
	
	public int nextInt() {
		fill();
		return Integer.parseInt(line.nextToken());
	}

	public long nextLong() {
		fill();
		return Long.parseLong(line.nextToken());
	}
	
	public double readDouble() {
		double d = 0;
		try {
			d = Double.parseDouble(input.readLine());
		} catch(IOException io) {io.printStackTrace(); System.exit(0);}
		return d;
	}
	
	public int readInt() {
		int i = 0;
		try {
			i = Integer.parseInt(input.readLine());
		} catch(IOException io) {io.printStackTrace(); System.exit(0);}
		return i;
	}
	
	public int[] readInts(int n) {
		int[] a = new int[n];
		for(int i=0; i<n; i++)
			a[i] = nextInt();
		return a;
	}
	
	public void fillInts(int[] a) {
		for(int i=0; i<a.length; i++)
			a[i] = nextInt();
	}
	
	public long readLong() {
		long l = 0;
		try {
			l = Long.parseLong(input.readLine());
		} catch(IOException io) {io.printStackTrace(); System.exit(0);}
		return l;
	}
	
	public String readLine() {
		String s = "";
		try {
			s = input.readLine();
		} catch(IOException io) {io.printStackTrace(); System.exit(0);}
		return s;
	}
}

class Writer {
	
	private BufferedWriter output;
	
	public Writer() {
		output = new BufferedWriter(new OutputStreamWriter(System.out));
	}
	
	public Writer(String s) {
		try {
			output = new BufferedWriter(new FileWriter(s));
		} catch(Exception ex) { ex.printStackTrace(); System.exit(0);}
	}
	
	public void println() {
		try {
			output.append("\n");
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}

	public void print(Object o) {
		try {
			output.append(o.toString());
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}
	
	public void println(Object o) {
		try {
			output.append(o.toString()+"\n");
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}

	public void printf(String format, Object... args) {
		try {
			output.append(String.format(format, args));
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}
	
	public void printfln(String format, Object... args) {
		try {
			output.append(String.format(format, args)+"\n");
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}
	
	public void flush() {
		try {
			output.flush();
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}
	
	public void close() {
		try {
			output.close();
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}
}