1 #include <iostream>
  2 #include <cstdio>
  3 #include <algorithm>
  4 #include <cstring>
  5 #include <queue>
  6 #define SIZE 40325
  7 using namespace std;
  8 
  9 const int fac[9] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320};
 10 struct ref{
 11     int parent;
 12     char op;
 13 }ans[SIZE];
 14 
 15 struct node{
 16     char s[10];
 17     int value;
 18     node(){}
 19     node(char * ss, const int v) : value(v){
 20         for(int i=0; i<8; ++i) *(s + i) = *(ss + i);
 21     }
 22 };
 23 
 24 bool vis[SIZE] = {0};
 25 int cantor(char * s){
 26     bool vis[10] = {0};
 27     int rec, ans = 0;
 28     for(int i=0; i<8; ++i){
 29         vis[s[i]] = 1, rec = 0;
 30         for(int j=1; j<s[i]; ++j)
 31             if(!vis[j]) ++rec;
 32         ans += rec * fac[7 - i];
 33     }
 34     return ans + 1;
 35 }
 36 
 37 void swap(char * s, const int posa, const int posb){
 38     char tmp = *(s + posa);
 39     *(s + posa) = *(s + posb);
 40     *(s + posb) = tmp;
 41 }
 42 
 43 void operate(char * s, const char type){
 44     if(type == 0){ for(int i=0; i<4; ++i) swap(s, i, 7-i); }
 45     else if(type == 1) for(int i=0; i<3; ++i) swap(s, i, 3), swap(s, 4, 7 - i);
 46     else { swap(s, 2, 5); swap(s, 1, 2); swap(s, 1, 6); }
 47 }
 48 
 49 void bfs(){
 50     int value, k = 0;
 51     node begin, now, next;
 52     for(int i=0; i<8; ++i) begin.s[i] = i+1;
 53     begin.value = cantor(begin.s);
 54     queue<node> q;
 55     q.push(begin);
 56     int rec = 0;
 57     while(q.size()){
 58         now = q.front(); q.pop();
 59         for(int i=0; i<3; ++i){
 60             next = now;
 61             operate(next.s, i);
 62             if(!vis[ value = cantor(next.s) ]){
 63                 vis[value] = 1;
 64                 q.push(node(next.s, value));
 65                 ans[value].parent = now.value;
 66                 ans[value].op = ‘A‘ + i;
 67             }
 68         }
 69     }
 70 }
 71 
 72 void deal(const int pos){
 73     if(ans[pos].parent == 1){
 74         putchar(ans[pos].op);
 75         return;
 76     }
 77     deal(ans[pos].parent);
 78     putchar(ans[pos].op);
 79 }
 80 
 81 void reflect(char * s, char * e){
 82     char reca[8], recb[8], ss[8];
 83     for(int i=0; i<8; ++i){
 84         reca[s[i]-1] = i, recb[e[i]-1] = i;
 85     }
 86     for(int i=0; i<8; ++i){
 87         *(e + recb[i]) = reca[i] + 1;
 88     }
 89 }
 90 
 91 int main(){
 92     //freopen("in", "r", stdin);
 93     char str[10], ptr[10];
 94     bfs();
 95     while(~scanf("%s%s", str, ptr)){
 96         if(!strcmp(str, ptr)){
 97             putchar(‘\n‘);
 98             continue;
 99         }
100         for(int i=0; i<8; ++i) str[i] -= ‘0‘, ptr[i] -= ‘0‘;
101         reflect(str, ptr);
102         deal(cantor(ptr));
103         putchar(‘\n‘);
104     }
105     return 0;
106 }