CodeForces 400A Inna and Choose Options

                                                                                                                         A. Inna and Choose Options

                                                                                                            time limit per test      1 second

                                                                                                            memory limit per test 256 megabytes

input

standard input

output

standard output

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 sizea × b from the cards he put on the table as follows: the firstb cards form the first row of the table, the secondb cards form the second row of the table and so on, the lastb cards form the last (numbera) 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 numbersa andb to choose. Help her win the game: print to her all the possible ways of numbersa, 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 thet tests on a separate line.

The description of each test is a string consisting of 12 characters, each character is either "X", or "O". Thei-th character of the string shows the character that is written on thei-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 paira, b. Next, print on this line the pairs in the formataxb. Print the pairs in the order of increasing first parameter (a). Separate the pairs in the line by whitespaces.

Sample test(s)

Input

4OXXXOXOOXOOXOXOXOXOXOXOXXXXXXXXXXXXXOOOOOOOOOOOO

Output

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

代码：

#include <iostream>#include <string.h>using namespace std;int main(){    int t;    char a[15];    int cnt;    int num[7];    cin>>t;    while(t--)    {        memset(num,0,sizeof(num));        cin>>a;        for(int i=0;i<12;i++)        if(a[i]=='X')        {            num[1]=1;            break;        }        for(int i=0;i<6;i++)        {            if(a[i]==a[i+6]&&a[i]=='X')            {                num[2]=1;                break;            }        }        for(int i=0;i<4;i++)        {            if(a[i]==a[i+4]&&a[i]==a[i+8]&&a[i]=='X')            {                num[3]=1;                break;            }        }        for(int i=0;i<3;i++)        {            if(a[i]==a[i+3]&&a[i]==a[i+6]&&a[i]==a[i+9]&&a[i]=='X')            {                num[4]=1;                break;            }        }        for(int i=0;i<2;i++)        {            if(a[i]==a[i+2]&&a[i]==a[i+4]&&a[i]==a[i+6]&&a[i]==a[i+8]&&a[i]==a[i+10]&&a[i]=='X')            {                num[5]=1;                break;            }        }        cnt=0;        for(int i=0;i<12;i++)        {            if(a[i]=='X')            cnt++;            if(cnt==12)            num[6]=1;        }        cnt=0;        for(int i=1;i<=6;i++)        {            if(num[i]) cnt++;        }        cout<<cnt;        if(num[1]) cout<<" "<<"1x12";        if(num[2]) cout<<" "<<"2x6";        if(num[3]) cout<<" "<<"3x4";        if(num[4]) cout<<" "<<"4x3";        if(num[5]) cout<<" "<<"6x2";        if(num[6]) cout<<" "<<"12x1";        cout<<endl;    }    return 0;}