#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include <debug.h>
#else
#define debug(...)
#endif
#define ft front
#define bk back
#define st first
#define nd second
#define ins insert
#define ers erase
#define pb push_back
#define pf push_front
#define _pb pop_back
#define _pf pop_front
#define lb lower_bound
#define ub upper_bound
#define mtp make_tuple
#define bg begin
#define ed end
#define all(x) (x).bg(), (x).ed()
#define sz(x) (int)(x).size()
typedef long long ll; typedef unsigned long long ull;
typedef double db; typedef long double ldb;
typedef pair<int, int> pi; typedef pair<ll, ll> pll;
typedef vector<int> vi; typedef vector<ll> vll; typedef vector<pi> vpi; typedef vector<pll> vpll;
typedef string str;
template<typename T> T gcd(T a, T b) { return (b == 0? a : gcd(b, a % b)); }
template<typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
#define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
#define FOS(i, r, l) for (int (i) = (r); (i) >= (l); --(i))
#define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
#define FSN(i, n) for (int (i) = (n) - 1; (i) >= 0; --(i))
#define EACH(i, x) for (auto &(i) : (x))
#define WHILE while
#define file "TEST"
mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());
ll rand(ll l, ll r) { return uniform_int_distribution<ll>(l, r)(rd); }
/*
----------------------------------------------------------------
END OF TEMPLATE
----------------------------------------------------------------
Tran The Bao - ghostwriter
Training for VOI23 gold medal
----------------------------------------------------------------
DIT ME CHUYEN BAO LOC
----------------------------------------------------------------
*/
struct Building {
int a, b;
bool rev;
Building() {}
Building(int a, int b, bool rev) : a(a), b(b), rev(rev) {}
};
const int N = 1e6 + 1;
int n, a[N], b[N], stat[N], cnt0 = 0, cnt1 = 0;
Building a1[N];
signed main() {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
// freopen(file".inp", "r", stdin);
// freopen(file".out", "w", stdout);
cin >> n;
FOR(i, 1, 2 * n) cin >> a[i];
FOR(i, 1, 2 * n) cin >> b[i];
memset(stat, -1, sizeof stat);
FOR(i, 1, 2 * n) {
bool rev = 0;
if (a[i] < b[i]) {
swap(a[i], b[i]);
rev = 1;
}
a1[i] = Building(a[i], b[i], rev);
}
FOS(i, 2 * n, 2) {
Building &pre = a1[i - 1], &cur = a1[i];
if (cur.a >= pre.a && cur.b >= pre.a) continue;
if (cur.a >= pre.a) {
if (cur.b >= pre.b) {
if (stat[i] != -1 && stat[i] != cur.rev) stat[i - 1] = pre.rev ^ 1;
// debug(i, stat[i], cur.rev ^ 1);
continue;
}
bool nstat = cur.rev;
if (stat[i] != -1 && stat[i] != nstat) {
cout << -1;
return 0;
}
stat[i] = nstat;
int pos = i + 1;
WHILE(pos <= 2 * n && stat[pos] == -1) {
Building &pre = a1[pos - 1], &cur = a1[pos];
if (cur.a >= pre.a && cur.b < pre.a && cur.b >= pre.b && stat[pos - 1] == pre.rev) {
stat[pos] = cur.rev;
++pos;
}
else break;
}
continue;
}
if (cur.a >= pre.b) {
if (cur.b < pre.b) {
bool nstat = cur.rev;
if (stat[i] != -1 && stat[i] != nstat) {
cout << -1;
return 0;
}
stat[i] = nstat;
int pos = i + 1;
WHILE(pos <= 2 * n && stat[pos] == -1) {
Building &pre = a1[pos - 1], &cur = a1[pos];
if (cur.a >= pre.a && cur.b < pre.a && cur.b >= pre.b && stat[pos - 1] == pre.rev) {
stat[pos] = cur.rev;
++pos;
}
else break;
}
nstat = pre.rev ^ 1;
stat[i - 1] = nstat;
continue;
}
bool nstat = pre.rev ^ 1;
stat[i - 1] = nstat;
continue;
}
cout << -1;
return 0;
}
// FOR(i, 1, 2 * n) {
// cerr << stat[i] << ' ';
// }
// cerr << '\n';
FOR(i, 1, 2 * n)
if (stat[i] == 0) ++cnt0;
else if (stat[i] == 1) ++cnt1;
if (cnt0 > n || cnt1 > n) {
cout << -1;
return 0;
}
FOR(i, 1, 2 * n) {
if (stat[i] != -1) continue;
cnt0 += (a1[i].rev? 0 : 1);
}
// debug(cnt0);
FOR(i, 1, 2 * n) {
if (stat[i] != -1) continue;
// debug(i, a1[i].rev, cnt0);
if (a1[i].a == a1[i].b) continue;
if (cnt0 < n) {
if (!a1[i].rev) continue;
stat[i] = 0;
++cnt0;
}
else if (cnt0 > n) {
if (a1[i].rev) continue;
stat[i] = 1;
--cnt0;
}
else stat[i] = a1[i].rev;
}
FOR(i, 1, 2 * n) {
if (a1[i].a != a1[i].b) continue;
if (cnt0 < n) {
stat[i] = 0;
++cnt0;
}
else if (cnt0 > n) {
stat[i] = 1;
--cnt0;
}
else stat[i] = a1[i].rev;
}
FOR(i, 1, 2 * n) cout << (stat[i]? 'B' : 'A');
return 0;
}
/*
2
6 4 6 8
3 4 8 9
----------------------------------------------------------------
From Benq:
stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
* DON'T GET STUCK ON ONE APPROACH
----------------------------------------------------------------
*/
