#include <stdio.h>
#include <string.h>
#include <malloc.h>


class Vector
{
public:
    Vector* next;
    char* representation;
    char* name;
};

Vector* all_vectors;

int nr_vec;
int nr_pos;
long counts[1000];

void read(FILE *f)
{
    char buf[1000];

    nr_vec = 0;
    nr_pos = 0;
    all_vectors = 0;
    Vector** ref_vector = &all_vectors;
    
    while (fgets(buf, 1000, f))
    {
        if (nr_pos == 0)
        {
            for (int i = 0; i < 1000 && (buf[i] == '0' || buf[i] == '1'); i++)
                nr_pos++;
            
            for (int i = 0; i < nr_pos; i++)
            {
                counts[i] = 0;
            }
        }
        
        nr_vec++;
        Vector *vector = new Vector;
        *ref_vector = vector;
        ref_vector = &vector->next;

        vector->representation = (char*)malloc(sizeof(char)*(nr_pos+1));
        strncpy(vector->representation, buf, nr_pos);
        vector->representation[nr_pos] = '\0';
        
        char *s = buf+nr_pos;
        while (*s == ' ')
            s++;
        int l = strlen(s);
        while (s[l-1] < ' ')
            s[--l] = '\0';
        vector->name = (char*)malloc(sizeof(char)*(l+1));
        strcpy(vector->name, s);
    }
}


int main(int argc, char* argv[])
{
    read(stdin);
    printf("%d %d\n", nr_vec, nr_pos);
    
    for (int i = 0; i < nr_pos; i++)
        counts[i] = 0;
        
    for (Vector* vector = all_vectors; vector != 0; vector = vector->next)
    {
        for (int i = 0; i < nr_pos; i++)
            if (vector->representation[i] == '1')
                counts[i]++;
    }

    for (bool progress = true; progress;)
    {
        progress = false;
    
        for (int i = 0; i < nr_pos; i++)
            for (int j = 0; j < nr_pos; j++)
                if (counts[i] < counts[j])
                {
                    if (counts[i] == 0)
                    {
                        printf("Unsolvable\n");
                        return 0;
                    }
                    
                    
                    bool implied = true;
                    
                    for (Vector* vector = all_vectors; vector != 0; vector = vector->next)
                    {
                        if (vector->representation[i] == '1' && vector->representation[j] == '0')
                        {
                            implied = false;
                            break;
                        }
                    }
                    
                    if (implied)
                    {
                        printf("Column %d implies column %d. Reduced number vectors with %d", i+1, j+1, counts[j]-counts[i]);  
                
                        for (Vector** ref_vector = &all_vectors; *ref_vector != 0; )
                        {
                            Vector* vector = *ref_vector;
                            
                            if (vector->representation[i] == '0' && vector->representation[j] == '1')
                            {
                                nr_vec--;
                                        
                                for (int k = 0; k < nr_pos; k++)
                                    if (vector->representation[k] == '1')
                                        counts[k]--;
                                        
                                *ref_vector = vector->next;
                            }
                            else
                                ref_vector = &vector->next;
                        }
                        
                        printf(" to %d.\n", nr_vec);
                        
                        progress = true;
                    }
                }
    }

    printf("\n\nLeft:\n");
    for (Vector* vector = all_vectors; vector != 0; vector = vector->next)
        printf("%s %s\n", vector->representation, vector->name);
        
    return 0;
}