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;
#define ll long long
#define pb push_back
#define ff first
#define ss second
#define all(s) s.begin(),s.end()
#define rall(s) s.rbegin(),s.rend()
int main(){
ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
ll n;
cin>>n;
ll a[2*n+5],b[2*n+5];
for(ll i=1;i<=2*n;i++){
cin>>a[i];
}
for(ll i=1;i<=2*n;i++){
cin>>b[i];
}
bool dp[2*n+5][n+5][2];//current building, A's count,i-th building type
memset(dp,false,sizeof dp);
ll bef[2*n+5][n+5][2];
memset(bef,-1,sizeof bef);
dp[1][1][0]=true;
dp[1][0][1]=true;
for(ll i=2;i<=2*n;i++){
for(ll j=0;j<=n;j++){
ll A=j,B=i-1-j;
if(A<0||B<0||A>n||B>n) continue;
if(A<n){
if(dp[i-1][A][0]==true&&a[i-1]<=a[i]){
dp[i][A+1][0]=true;
bef[i][A+1][0]=0;
}
if(dp[i-1][A][1]==true&&b[i-1]<=a[i]){
dp[i][A+1][0]=true;
bef[i][A+1][0]=1;
}
}
if(B<n){
if(dp[i-1][A][0]==true&&a[i-1]<=b[i]){
dp[i][A][1]=true;
bef[i][A][1]=0;
}
if(dp[i-1][A][1]==true&&b[i-1]<=b[i]){
dp[i][A][1]=true;
bef[i][A][1]=1;
}
}
}
}
if(!dp[2*n][n][0]&&!dp[2*n][n][1]){
cout<<-1;
return 0;
}
string s="";
ll pos=0,cnt=n;
if(dp[2*n][n][1]){
pos=1;
}
for(ll i=2*n;i>=1;i--){
if(pos==0){
s+='A';
}
else{
s+='B';
}
ll p=pos;
if(i>1){
pos=bef[i][cnt][pos];
}
if(p==0) cnt--;
}
reverse(all(s));
cout<<s;
}
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