This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")
#include<bits/stdc++.h>
using namespace std;
const int maxn=1000000+10;
int n;
int dpl[maxn][2],dpr[maxn][2],all[maxn][2];
string res;
void cal(int ind,int vas,int ted=n){
while(true){
if(vas==1){
res.push_back('B');
ted--;
}
else{
res.push_back('A');
}
if(ind==0){
return ;
}
if(all[ind-1][vas]<=all[ind][vas]&&dpl[ind-1][vas]<=ted&&dpr[ind-1][vas]>=ted){
ind--;
}
else{
vas^=1;
ind--;
}
}
}
int main(){
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin>>n;
n*=2;
for(int i=0;i<n;i++){
cin>>all[i][0];
}
for(int i=0;i<n;i++){
cin>>all[i][1];
}
dpl[0][0]=dpr[0][0]=0;
dpl[0][1]=dpr[0][1]=1;
for(int i=1;i<n;i++){
for(int j=0;j<2;j++){
dpl[i][j]=maxn+10;
dpr[i][j]=-1;
if(dpr[i-1][j]!=-1&&all[i-1][j]<=all[i][j]){
dpl[i][j]=dpl[i-1][j];
dpr[i][j]=dpr[i-1][j];
}
if(dpr[i-1][j^1]!=-1&&all[i-1][j^1]<=all[i][j]){
dpl[i][j]=min(dpl[i][j],dpl[i-1][j^1]);
dpr[i][j]=max(dpr[i][j],dpr[i-1][j^1]);
}
if(dpr[i][j]!=-1&&j==1){
dpr[i][j]++;
dpl[i][j]++;
}
// cout<<i<<" "<<j<<" "<<dpl[i][j]<<" "<<dpr[i][j]<<"\n";
}
}
n/=2;
if(n>=dpl[2*n-1][0]&&n<=dpr[2*n-1][0]){
cal(2*n-1,0);
reverse(res.begin(),res.end());
cout<<res<<"\n";
return 0;
}
if(n>=dpl[2*n-1][1]&&n<=dpr[2*n-1][1]){
cal(2*n-1,1);
reverse(res.begin(),res.end());
cout<<res<<"\n";
return 0;
}
cout<<-1<<"\n";
return 0;
}
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