This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<bits/stdc++.h>
using namespace std;
const int N = 5e5;
const int inf = 2e9;
struct xy{
int x,y;
}v[N];
bool ans[N];
int main(){
bool ok = 1;
int prv = -1;
int cnt = 0;
int n;
cin>>n;
for(int i = 0;i < 2*n;i++){
cin>>v[i].x;
}
for(int i = 0;i < 2*n;i++){
cin>>v[i].y;
}
for(int i = 0;i < 2*n;i++){
if(v[i].x <= v[i].y){
///v[i].x
if(prv <= v[i].x){
ans[i] = 0;
prv = v[i].x;
}else if(prv <= v[i].y){
ans[i] = 1;
prv = v[i].y;
cnt++;
}else ok = 0;
}else{
if(prv <= v[i].y){
ans[i] = 1;
prv = v[i].y;
cnt++;
}else if(prv <= v[i].x){
ans[i] = 0;
prv = v[i].x;
}else ok = 0;
}
prv = (ans[i] == 0?v[i].x:v[i].y);
}
if(cnt == n && ok){
for(int i = 0;i < 2*n;i++){
cout<<(ans[i] == 0?"A":"B");
}
return 0;
}
prv = inf;
for(int i = 2*n - 1;i >= 0;i--){
cnt-=ans[i];
if(v[i].x <= v[i].y){
if(prv >= v[i].y){
ans[i] = 1;
prv = v[i].y;
}else if(prv >= v[i].x){
ans[i] = 0;
prv = v[i].x;
}else ok = 0;
}else{
if(prv >= v[i].x){
ans[i] = 0;
prv = v[i].x;
}else if(prv >= v[i].y){
ans[i] = 1;
prv = v[i].y;
}else ok = 0;
}
cnt+=ans[i];
prv = (ans[i] == 0?v[i].x:v[i].y);
if(cnt == n && ok){
for(int i = 0;i < 2*n;i++){
cout<<(ans[i] == 0?"A":"B");
}
return 0;
}
}
cout<<-1;
return 0;
}
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