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>
typedef long long ll;
#define f first
#define s second
#define pb push_back
#define ep emplace
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define uniquev(v) sort(all(v)), (v).resize(unique(all(v)) - (v).begin())
#define mem(f,x) memset(f , x , sizeof(f))
#define sz(x) (int)(x).size()
#define __lcm(a, b) (1ll * ((a) / __gcd((a), (b))) * (b))
#define mxx *max_element
#define mnn *min_element
#define cntbit(x) __builtin_popcountll(x)
using namespace std;
const int N = 1e6 + 100;
int A[N][2], mx[N][2], mi[N][2];
int c[2] = {-1, 1};
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int n;
cin >> n;
int sz = n * 2;
for (int i = 1; i <= sz; i++)
cin >> A[i][0];
for (int i = 1; i <= sz; i++)
cin >> A[i][1];
for (int i = 1; i <= sz; i++) {
mx[i][0] = mx[i][1] = -1e9;
mi[i][0] = mi[i][1] = 1e9;
}
mi[sz][0] = mx[sz][0] = -1;
mi[sz][1] = mx[sz][1] = 1;
for (int i = sz - 1; i >= 1; i--) {
for (int j = 0; j < 2; j++) {
for (int k = 0; k < 2; k++) {
if (A[i][j] <= A[i + 1][k]) {
mx[i][j] = max(mx[i][j], mx[i + 1][k] + c[j]);
mi[i][j] = min(mi[i][j], mi[i + 1][k] + c[j]);
}
}
}
}
int x = 1, y = 0, all = 0;
string ans;
if (mi[x][y] > 0 || mx[x][y] < 0) {
y = 1;
}
if (mi[x][y] > 0 || mx[x][y] < 0) {
cout << -1 << '\n';
return 0;
}
while (x <= sz) {
if (y == 0) {
ans += "A";
all--;
} else {
ans += "B";
all++;
}
if (x == sz)
break;
int t = 1;
for (int k = 0; k < 2; k++) {
if (A[x][y] <= A[x + 1][k]) {
if (mi[x + 1][k] + all <= 0 && mx[x + 1][k] + all >= 0) {
t = k;
break;
}
}
}
x++;
y = t;
}
cout << ans << '\n';
}
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