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>
#define fi first
#define se second
using namespace std;
const int N = 500005;
int n, a[2 * N][2];
bool chk[2 * N][2];
string ans;
pair<int, int> r[2 * N][2];
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n;
for (int it = 0; it < 2; it++) {
for (int i = 1; i <= 2 * n; i++) {
cin >> a[i][it];
}
}
chk[0][0] = true;
for (int i = 1; i <= 2 * n; i++) {
for (int it = 0; it < 2; it++) {
for (int j = 0; j < 2; j++) {
if (chk[i - 1][j] && a[i - 1][j] <= a[i][it]) {
if (!chk[i][it]) {
chk[i][it] = true;
r[i][it] = {r[i - 1][j].fi + it, r[i - 1][j].se + it};
} else {
r[i][it].fi = min(r[i][it].fi, r[i - 1][j].fi + it);
r[i][it].se = max(r[i][it].se, r[i - 1][j].se + it);
}
}
}
}
}
for (int it = 0; it < 2; it++) {
if (chk[2 * n][it] && r[2 * n][it].fi <= n && n <= r[2 * n][it].se) {
for (int i = 2 * n, cur = n; i >= 1; i--) {
ans.push_back('A' + it);
cur -= it;
for (int j = 0; j < 2; j++) {
if (chk[i - 1][j] && a[i - 1][j] <= a[i][it] && r[i - 1][j].fi <= cur && cur <= r[i - 1][j].se) {
it = j;
break;
}
}
}
reverse(ans.begin(), ans.end());
return cout << ans, 0;
}
}
cout << -1;
}
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