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 INF = 1e7;
int main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
int n;
cin >> n;
vector<vector<int>> v(2, vector<int>(2*n));
for(int b = 0; b < 2; ++b) for(int i = 0; i < 2*n; ++i) cin >> v[1-b][i];
vector<vector<int>> mi(2, vector<int>(2*n, INF)), ma(2, vector<int>(2*n, -INF));
mi[0][2*n-1] = ma[0][2*n-1] = 0;
mi[1][2*n-1] = ma[1][2*n-1] = 1;
for(int i = 2*n-2; i >= 0; --i){
for(int j = 0; j < 2; ++j){
for(int k = 0; k < 2; ++k){
if(v[j][i] <= v[k][i+1]){
mi[j][i] = min(mi[j][i], mi[k][i+1]+j);
ma[j][i] = max(ma[j][i], ma[k][i+1]+j);
}
}
}
}
string ans;
if(mi[0][0] <= n && n <= ma[0][0]) ans += 'B';
else if(mi[1][0] <= n && n <= ma[1][0]) ans += 'A';
if(ans.empty()) cout << "-1\n";
else{
int j = (ans=="A");
int cnt = n-j;
for(int i = 1; i < 2*n; ++i){
for(int k = 0; k < 2; ++k){
if(v[j][i-1] <= v[k][i]){
if(mi[k][i] <= cnt && cnt <= ma[k][i]){
cnt -= k;
j = k;
ans += 'A'+(1-k);
break;
}
}
}
}
cout << ans << "\n";
}
}
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