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 fi first
#define se second
#define ll long long
#define pb push_back
#define ii pair<int,int>
const int nax=5e5+5;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int dp[2][nax][2];
int tab[2][nax];
int main() {
int n;
cin>>n;
n*=2;
for (int i = 0; i < 2; ++i)
{
for (int j = 1; j <= n; ++j)
{
cin>>tab[i][j];
}
}
for (int i = 1; i <= n; ++i)
{
for (int j = 0; j < 2; ++j)
{
dp[j][i][0]=n+1;
dp[j][i][1]=-1;
for (int k = 0; k < 2; ++k)
{
if(tab[j][i]>=tab[k][i-1]){
dp[j][i][0]=min(dp[j][i][0],dp[k][i-1][0]+j);
dp[j][i][1]=max(dp[j][i][1],dp[k][i-1][1]+j);
}
}
}
}
int lst=-1;
for (int i = 0; i < 2; ++i)
{
if(dp[i][n][0]<=n/2&&n/2<=dp[i][n][1]){
lst=i;
}
}
if(lst<0){
cout <<-1<<endl;
}else{
string ans="";
int c=n/2;
while(n){
ans.pb(char('A'+lst));
c-=lst;
lst=(tab[1][n-1]<=tab[lst][n]&&dp[1][n-1][0]<=c&&c<=dp[1][n-1][1]);
n--;
}
reverse(ans.begin(),ans.end());
cout <<ans<<endl;
}
}
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