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 = 1e5 + 7, INF = 1e9 + 10;
int n, a[N][2];
int mn[N][2], mx[N][2];
int main() {
#ifdef LOCAL
freopen("input.txt", "r", stdin);
#endif
ios::sync_with_stdio(false);
cin.tie(0);
cin >> n;
a[0][0] = a[0][1] = -INF;
for (int i = 0; i < 2; i++) {
for (int j = 1; j <= 2 * n; j++) cin >> a[j][i];
}
for (int i = 0; i <= 2 * n; i++) {
for (int j = 0; j < 2; j++) {
mn[i][j] = INF;
mx[i][j] = -INF;
}
}
for (int i = 0; i < 2; i++) mn[0][i] = mx[0][i] = 0;
for (int i = 1; i <= 2 * n; i++) {
for (int j = 0; j < 2; j++) {
for (int k = 0; k < 2; k++) {
if (a[i - 1][k] <= a[i][j]) {
if (mn[i - 1][k] != INF) mn[i][j] = min(mn[i][j], mn[i - 1][k] + j);
if (mx[i - 1][k] != -INF) mx[i][j] = max(mx[i][j], mx[i - 1][k] + j);
}
}
}
}
int j = -1;
for (int i = 0; i < 2; i++) {
if (mn[2 * n][i] <= n && n <= mx[2 * n][i]) {
j = i;
break;
}
}
if (j == -1) {
cout << -1;
return 0;
}
string ans = "";
int cur = n;
for (int i = 2 * n; i > 0; i--) {
cur -= j;
ans.push_back('A' + j);
for (int k = 0; k < 2; k++) {
if (mn[i - 1][k] <= cur && cur <= mx[i - 1][k]) {
j = k;
break;
}
}
}
reverse(ans.begin(), ans.end());
cout << ans << endl;
return 0;
}
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