sicily 1150,1151

// Problem#: 1151
// Submission#: 2982372
// The source code is licensed under Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License
// URI: http://creativecommons.org/licenses/by-nc-sa/3.0/ // All Copyright reserved by Informatic Lab of Sun Yat-sen University
#include<iostream>
#include<queue>
#include<stdio.h>
using namespace std;
struct node {
  int a;
  int b;
  string path;
  int sum;

  node() {
    sum = 0;
  }
};

struct hash {
    int n;
    hash *next;
};

node end;
queue<node> q;
int n;
bool sign;
hash *ju[10000];
bool cmp(node temp) {
  if(temp.a == end.a && temp.b == end.b){
    sign = 1;
    return true;
  } else {
    return false;
  }
}

bool judge(node temp) {
    if(ju[temp.a] == NULL) {
        ju[temp.a] = new hash();
        (ju[temp.a])->n = temp.b;
        (ju[temp.a])->next = NULL;
        return true;
    } else {
        hash *p;
        p = ju[temp.a];
        if(p->n == temp.b) {
            return false;
        } else {
            while(p->next != NULL) {
                p = p->next;
                if(p->n == temp.b) {
                    return false;
                }
            }
            p->next= new hash();
            p = p->next;
            p->n = temp.b;
            p->next = NULL;
            return true;
        }
    }
}

void Achange(node temp) {
  if(sign == 0 && temp.sum < n) {
        int a1;
        a1 = temp.a;
        temp.a = temp.b;
        temp.b = a1;
        (temp.path).push_back('A');
        temp.sum++;
        if(cmp(temp)) {
          end.path = temp.path;
          end.sum = temp.sum;  
        } else {
          if(judge(temp)) {
            q.push(temp);
          }
        }
      }
}

void Bchange(node temp) {
  if(sign == 0 && temp.sum < n) {    
        int a1;
        int b1;
        a1 = temp.a % 10;
        b1 = temp.b % 10;
        temp.a = temp.a/10 + a1*1000;
        temp.b = temp.b/10 + b1*1000;
        (temp.path).push_back('B');
        temp.sum++;
        if(cmp(temp)) {
          end.path = temp.path;
          end.sum = temp.sum;  
        } else {
            if(judge(temp)) {
            q.push(temp);
          }
        }

   }
}

void Cchange(node temp) {
  if(sign == 0 && temp.sum < n) {
        int g1,s1,b1,q1,g2,s2,b2,q2;
        g1 = temp.a%10;
        s1 = (temp.a%100)/10;
        b1 = (temp.a%1000)/100;
        q1 = temp.a/1000;
        g2 = temp.b%10;
        s2 = (temp.b%100)/10;
        b2 = (temp.b%1000)/100;
        q2 = temp.b/1000;
        temp.a = q1*1000 + b2*100 + b1*10 +g1;
        temp.b = q2*1000 + s2*100 + s1*10 + g2;
        (temp.path).push_back('C');
        temp.sum++;
        if(cmp(temp)) {
          end.path = temp.path;
          end.sum = temp.sum;  
        } else {
        if(judge(temp)) {
            q.push(temp);
          }
        }
    }
}

int main() {
  while(cin>>n && n != -1) {
    for(int i = 0; i < 10000; i++) {
        ju[i] = NULL;
    }
    int a = 0;
    int b = 0;
    char c;
    c=getchar();
    c=getchar();
    while(c != '\n') {
      if(c != ' ') {
        a = a*10 + (int)(c - '0');
      }
      c = getchar();
    }
    c = getchar();
    while(c != '\n') {
      if(c != ' ') {
        b = b*10 + (int)(c - '0');
      }
      c = getchar();
    }
    node start;
    start.sum = 0;
    start.a = 1234;
    start.b = 8765;
    end.a = a;
    end.b = b;
    end.sum = 0;
    end.path = "";
    q.push(start);
    sign = 0;
    ju[1234] = new hash();
    (ju[1234])->n = 8765;
    (ju[1234])->next = NULL;
    if(cmp(start)) {
    }
    while(!q.empty() && sign == 0) {
      Achange(q.front());
      Bchange(q.front());
      Cchange(q.front());
      q.pop();
    }

    if(sign == 1) {
      cout << end.sum << "  " << end.path << endl;
    } else {
      cout << "-1" <<endl;
    }
  }
}