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>
#define pb push_back
#define mp make_pair
#define x first
#define y second
using namespace std;
typedef long long ll;
int mas[5][1000005], ans[1000005], type[1000005];
int main()
{
//freopen("input.txt", "r", stdin);
//freopen("output.txt", "w", stdout);
ios_base::sync_with_stdio(0); cin.tie(0);
int n;
cin >> n;
for (int i = 1; i <= 2 * n; i++) cin >> mas[1][i];
for (int i = 1; i <= 2 * n; i++) cin >> mas[2][i];
for (int i = 1; i <= 2 * n; i++) ans[i] = min(mas[1][i], mas[2][i]);
for (int i = 2; i <= 2 * n; i++)
{
if (ans[i] < ans[i - 1]) ans[i] = max(mas[1][i], mas[2][i]);
if (ans[i] < ans[i - 1]) cout << "-1\n", exit(0);
}
int bal = 0;
for (int i = 1; i <= 2 * n; i++)
if (ans[i] == mas[1][i]) bal++, type[i] = 1;
else bal--, type[i] = 2;
int uk = 1;
while (uk <= 2 * n && bal != 0)
{
int cop = uk;
while (cop + 1 <= 2 * n && max(mas[1][cop + 1], mas[2][cop + 1]) >= max(mas[1][cop], mas[2][cop])
&& min(mas[1][cop + 1], mas[2][cop + 1]) < max(mas[1][cop], mas[2][cop])) cop++;
if (cop == 2 * n || max(mas[1][cop], mas[2][cop]) <= min(mas[1][cop + 1], mas[2][cop + 1]))
{
int mx = 0, del = 0;
for (int i = cop; i >= uk; i--)
{
if (type[i] == 1) del -= 2;
else del += 2;
if (bal > 0) mx = min(mx, del);
else mx = max(mx, del);
}
del = 0;
if (bal > 0 && bal + mx < 0) mx = -bal;
if (bal < 0 && bal + mx > 0) mx = -bal;
if (mx != 0)
{
for (int i = cop; i >= uk; i--)
{
if (type[i] == 1) del -= 2;
else del += 2;
type[i] = 3 - type[i];
if (del == mx) break;
}
}
bal += mx;
}
uk = cop + 1;
}
if (bal != 0) cout << "-1\n", exit(0);
for (int i = 1; i <= 2 * n; i++)
if (type[i] == 1) cout << 'A';
else cout << 'B';
cout << '\n';
return 0;
}
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