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;
typedef long double ld;
typedef long long ll;
#define rep(a, b) for(int a = 0; a < (b); ++a)
#define st first
#define nd second
#define pb push_back
#define all(a) a.begin(), a.end()
const ll LIM=1e6+7;
ll T[LIM][2], jaki[LIM], czy[LIM];
int co(int x) {
if(jaki[x]) return -1;
return 1;
}
int main() {
ios_base::sync_with_stdio(0); cin.tie(0);
ll n;
cin >> n; n*=2;
rep(i, n) {
cin >> T[i][0];
T[i][0]*=2*n;
T[i][0]+=(ll)(2*i);
}
rep(i, n) {
cin >> T[i][1];
T[i][1]*=2*n;
T[i][1]+=(ll)(2*i+1);
}
ll lst=0, sum=0;
rep(i, n) {
if(T[i][0]<T[i][1]) {
if(lst<T[i][0]) {
lst=T[i][0];
} else if(lst<T[i][1]) {
lst=T[i][1];
jaki[i]=1;
} else {
cout << -1 << '\n';
return 0;
}
} else {
if(lst<T[i][1]) {
lst=T[i][1];
jaki[i]=1;
} else if(lst<T[i][0]) {
lst=T[i][0];
} else {
cout << -1 << '\n';
return 0;
}
}
sum+=co(i);
}
int p=n-1, bil=0;
for(int i=n-1; i>=0; --i) {
if(T[i][jaki[i]]>T[i][jaki[i]^1] || (i<n-1 && T[i][jaki[i]^1]>max(T[i+1][0], T[i+1][1]))) {
p=i-1; bil=0;
continue;
}
if(i==n-1 || T[i][jaki[i]^1]<T[i+1][jaki[i+1]]) {
p=i; bil=0;
}
bil+=co(i);
if(abs(sum-2*bil)<abs(sum)) {
sum-=2*bil;
for(int j=i; j<=p; ++j) jaki[j]^=1;
p=i-1; bil=0;
}
}
if(sum!=0) {
cout << -1 << '\n';
return 0;
}
rep(i, n) cout << (jaki[i]?"B":"A");
cout << '\n';
}
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