This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
// In the name of God
//-MILY-
#include<bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define mp make_pair
typedef long long ll;
const int N = 1e6 + 5;
int n, a[N], b[N];
pair<int, int> P[N][2];
bool mark[N];
pair<int, int> unite(pair<int, int> x, pair<int, int> y) {
if (x.fi == -1)
return y;
if (y.fi == -1)
return x;
return mp(min(x.fi, y.fi), max(x.se, y.se));
}
void solve() {
cin >> n;
int m = n;
n *= 2;
for (int i = 0; i < n; i++)
cin >> a[i];
for (int i = 0; i < n; i++)
cin >> b[i];
P[0][0] = mp(1, 1);
P[0][1] = mp(0, 0);
for (int i = 1; i < n; i++) {
int x = a[i], y = b[i];
int xp = a[i - 1], yp = b[i - 1];
P[i][0] = P[i][1] = mp(-1, -1);
if (P[i - 1][0].fi != -1) {
if (x >= xp) {
P[i][0] = P[i - 1][0];
}
if (y >= xp)
P[i][1] = P[i - 1][0];
}
if (P[i - 1][1].fi != -1) {
if (x >= yp) {
P[i][0] = unite(P[i][0], P[i - 1][1]);
}
if (y >= yp)
P[i][1] = unite(P[i][1], P[i - 1][1]);
}
if (P[i][0].fi != -1) {
P[i][0].fi++;
P[i][0].se++;
}
}
pair<int, int> res = unite(P[n - 1][0], P[n - 1][1]);
if (m < res.fi || m > res.se) {
cout << -1 << '\n';
return;
}
string ans;
bool x = false;
if (m >= P[n - 1][1].fi && m <= P[n - 1][1].se) {
x = true;
}
int i = n - 1;
while (i > 0) {
ans += char(x + 'A');
m -= !x;
int val = x ? b[i] : a[i];
if (a[i - 1] <= val && m >= P[i - 1][0].fi && m <= P[i - 1][0].se)
x = false;
else if (b[i - 1] <= val && m >= P[i - 1][1].fi && m <= P[i - 1][1].se)
x = true;
i--;
}
ans += char(x + 'A');
reverse(ans.begin(), ans.end());
cout << ans << '\n';
}
int32_t main() {
ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
solve();
return 0;
}
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