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 = 1e6 + 1 , oo = 1e9;
int n;
int A[N][2] , mn[N][2] , mx[N][2];
char t[2] = {'A' , 'B'};
int main(){
   ios_base::sync_with_stdio(false);
   cin.tie(0);
   cout.tie(0);
   cin >> n;
   n *= 2;
   for(int x = 0;x < 2;x ++){
      for(int i = 1;i <= n;i ++){
         cin >> A[i][x];
      }
   }
   for(int i = 1;i <= n;i ++){
      for(int x = 0;x < 2;x ++){
         mn[i][x] = oo;
         mx[i][x] = 0;
         for(int y = 0;y < 2;y ++){
            if(A[i][x] >= A[i - 1][y]){
               mn[i][x] = min(mn[i][x] , mn[i - 1][y] + !x);
               mx[i][x] = max(mx[i][x] , mx[i - 1][y] + !x);
            }
         }
      }
   }
   for(int x = 0;x < 2;x ++){
      if(mn[n][x] <= n / 2 && n / 2 <= mx[n][x]){
         int ans[n + 1];
         int v = n , e = x , cnt = 0;
         while(v >= 1){
            ans[v] = e;
            cnt += !e;
            --v;
            if(A[v + 1][e] >= A[v][0] && mn[v][0] + cnt <= n / 2 && n / 2 <= mx[v][0] + cnt){
               e = 0;
            }else{
               e = 1;
            }
         }
         for(int i = 1;i <= n;i ++){
           cout << t[ans[i]];
         }
         cout << endl;
         return 0;
      }
   }
   cout << -1 << endl;
}
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