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;
#define chkmin(a, b) a = min(a, b);
#define chkmax(a, b) a = max(a, b)
//#define int long long
#define size(a) (int)a.size()
#define all(a) a.begin(), a.end()
#define pii pair<int, int>
#define fi first
#define se second
#define pb emplace_back
#define mp make_pair
const int inf = 1e9;
const int max_n = 1e6 + 3;
int n;
int A[max_n], B[max_n];
pii dp[max_n][2];
void run() {
cin >> n;
n *= 2;
for (int i = 0; i < n; ++i)
cin >> A[i];
for (int i = 0; i < n; ++i)
cin >> B[i];
for (int i = 0; i < n; ++i)
dp[i][0] = dp[i][1] = mp(inf, -inf);
dp[0][0] = mp(0, 0);
dp[0][1] = mp(1, 1);
for (int i = 0; i < n - 1; ++i) {
for (int msk = 0; msk < 4; ++msk) {
if (((msk & 1) ? B[i] : A[i]) <= (msk & 2 ? B[i + 1] : A[i + 1])) {
chkmin(dp[i + 1][msk >> 1 & 1].fi, dp[i][msk & 1].fi);
chkmax(dp[i + 1][msk >> 1 & 1].se, dp[i][msk & 1].se);
}
}
++dp[i + 1][1].fi;
++dp[i + 1][1].se;
}
//for (int i = 0; i < n; ++i)
// cout << dp[i][0].fi << " " << dp[i][0].se << " " << dp[i][1].fi << " " << dp[i][1].se << endl;
if ((dp[n - 1][0].fi > n / 2 || dp[n - 1][0].se < n / 2) && (dp[n - 1][1].fi > n / 2 || dp[n - 1][1].se < n / 2)) {
cout << -1;
return;
}
vector<int> res(n);
int oth = n / 2;
int lst = inf;
for (int i = n - 1; i >= 0; --i) {
if (dp[i][0].fi <= oth && dp[i][0].se >= oth && A[i] <= lst) lst = A[i];
else {
--oth;
res[i] = 1;
lst = B[i];
}
}
for (int i : res)
cout << char('A' + i);
cout << endl;
}
signed main() {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
#ifdef ahahaha
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
run();
}
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