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;
const int MAXN = 1e6 + 5;
const int INF = 1e9;
int n;
int A[MAXN][2], l[MAXN][2], r[MAXN][2];
int ans[MAXN];
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
cin >> n;
for(int i = 1; i <= 2 * n; i++)
{
cin >> A[i][0];
}
for(int i = 1; i <= 2 * n; i++)
{
cin >> A[i][1];
}
for(int i = 1; i <= 2 * n; i++)
{
for(int j = 0; j < 2; j++)
{
l[i][j] = INF; r[i][j] = -INF;
for(int k = 0; k < 2; k++)
{
if(A[i][j] >= A[i - 1][k])
{
l[i][j] = min(l[i][j], l[i - 1][k] + j);
r[i][j] = max(r[i][j], r[i - 1][k] + j);
}
}
}
}
int root = -1, cntb = n;
for(int i = 0; i < 2; i++)
{
if(l[2 * n][i] <= cntb and r[2 * n][i] >= cntb)
{
root = i;
}
}
if(root == -1)
{
cout << -1 << '\n';
}
else
{
for(int i = 2 * n; i >= 1; i--)
{
for(int j = 0; j < 2; j++)
{
if(A[i][root] >= A[i - 1][j] and cntb - root >= l[i - 1][j] and cntb - root <= r[i - 1][j])
{
ans[i] = root;
cntb -= root;
root = j;
break;
}
}
}
for(int i = 1; i <= 2 * n; i++)
{
cout << char(ans[i] + 'A');
}
cout << '\n';
}
}
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