#include <iostream>
#include <algorithm>
#include <vector>
const int MAXN = 1e6 + 2;
const int INFTY = 2e9;
int plan[2][MAXN];
int color[MAXN];
struct Ans {
Ans() : size(-INFTY), pos(-1), prev(-1) {}
Ans(int s, int p, int pr) : size(s), pos(p), prev(pr) {};
int size, pos, prev;
bool operator >(const Ans &other) const
{
return (size > other.size);
}
} lis[2][MAXN];
std::vector<int> findlis(int size)
{
std::fill_n((Ans *)lis, 2 * MAXN, Ans());
lis[0][0] = Ans(0, 0, -1);
for (int iPos = 1; iPos <= size; iPos++)
{
Ans b0 = lis[0][iPos - 1];
Ans b1 = lis[1][iPos - 1];
if (plan[0][iPos - 1] <= plan[1][iPos] && b0 > lis[1][iPos])
lis[1][iPos] = b0;
if (plan[1][iPos - 1] <= plan[1][iPos] && b1 > lis[1][iPos])
lis[1][iPos] = b1;
b0.size++; b1.size++;
b0.prev = b0.pos;
b1.prev = b1.pos;
b0.pos = b1.pos = iPos;
if (plan[0][iPos - 1] <= plan[0][iPos] && b0 > lis[0][iPos])
lis[0][iPos] = b0;
if (plan[1][iPos - 1] <= plan[0][iPos] && b1 > lis[0][iPos])
lis[0][iPos] = b1;
}
std::vector<int> seq;
int pos = size;
while (pos != -1)
{
seq.emplace_back(pos);
pos = lis[0][pos].prev;
}
if (seq.back() != 0)
return {};
std::vector<int> choice;
pos = 0;
while (seq.size() > 1)
{
choice.emplace_back(0);
seq.pop_back();
for (pos++; pos < seq.back(); pos++)
choice.emplace_back(1);
}
choice.emplace_back(0);
return choice;
}
int cnt0(std::vector<int> vec)
{
int c = 0;
for (int i : vec)
c += (i == 0);
return c - 2;
}
int main()
{
std::ios::sync_with_stdio(false);
std::cout.tie(nullptr);
std::cin.tie(nullptr);
int half; std::cin >> half;
int build = half * 2;
for (int iPlan = 0; iPlan < 2; iPlan++)
{
plan[iPlan][build + 1] = INFTY;
for (int iBuild = 1; iBuild <= build; iBuild++)
std::cin >> plan[iPlan][iBuild];
}
std::vector<int> choiceA = findlis(build + 1);
for (int iBuild = 1; iBuild <= build; iBuild++)
std::swap(plan[0][iBuild], plan[1][iBuild]);
std::vector<int> choiceB = findlis(build + 1);
if (choiceA.empty() || choiceB.empty())
{
std::cout << "-1\n";
return 0;
}
for (int &choose : choiceB)
choose ^= 1;
choiceB[0] = choiceB[build + 1] = 0;
int maxA = cnt0(choiceA);
int minA = cnt0(choiceB);
if (maxA < half || minA > half)
{
std::cout << "-1\n";
return 0;
}
std::vector<int> eq;
for (int iPos = 0; iPos < build + 2; iPos++)
if (choiceA[iPos] == choiceB[iPos])
eq.emplace_back(iPos);
for (int iSpl = 0; maxA > half; iSpl++)
{
int chg = 0;
for (int iPos = eq[iSpl] + 1; iPos < eq[iSpl + 1]; iPos++)
chg += choiceA[iPos] - choiceB[iPos];
if (maxA + chg >= half)
{
maxA += chg;
for (int iPos = eq[iSpl] + 1; iPos < eq[iSpl + 1]; iPos++)
choiceA[iPos] ^= 1;
continue;
}
for (int iPos = eq[iSpl] + 1; iPos < eq[iSpl + 1]; iPos++)
color[iPos] = (plan[choiceA[iPos]][iPos] < plan[choiceB[iPos]][iPos]);
for (int iPos = eq[iSpl] + 1; iPos < eq[iSpl + 1] && maxA > half; iPos++)
if (color[iPos] == 1)
{
maxA += choiceA[iPos] - choiceB[iPos];
choiceA[iPos] ^= 1;
}
for (int iPos = eq[iSpl + 1] - 1; iPos > eq[iSpl] && maxA > half; iPos--)
if (color[iPos] == 0)
{
maxA += choiceA[iPos] - choiceB[iPos];
choiceA[iPos] ^= 1;
}
}
for (int iPos = 1; iPos <= build; iPos++)
std::cout << (char)('A' + choiceA[iPos]);
std::cout << '\n';
return 0;
}
