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;
#define int int64_t
signed main() {
cin.tie(0);
ios_base::sync_with_stdio(0);
int n; cin >> n;
n*=2;
vector<int> a(n), b(n);
for (int &i: a) cin >> i;
for (int &i: b) cin >> i;
int la=0, ra=0;
int lb=0, rb=0;
int curra = 0;
int currb = 0;
vector<array<int, 4>> bcktrck(n);
for (int i = 0; i<n; i++) {
bcktrck[i] = {la, ra, lb, rb};
int nla=1e18, nra=-1e18;
if (a[i] >= curra) {
nla=min(nla,la+1);
nra=max(nra,ra+1);
}
if (a[i] >= currb) {
nla=min(nla,lb+1);
nra=max(nra,rb+1);
}
int nlb=1e18, nrb=-1e18;
if (b[i] >= curra) {
nlb=min(nlb,la);
nrb=max(nrb,ra);
}
if (b[i] >= currb) {
nlb=min(nlb,lb);
nrb=max(nrb,rb);
}
la=nla;
ra=nra;
lb=nlb;
rb=nrb;
curra = a[i];
currb = b[i];
}
bcktrck.push_back({la, ra, lb, rb});
if (!(min(la, lb) <= n/2 && n/2 <= max(ra, rb))) {
cout << -1 << "\n";
return 0;
}
int currReq = n/2;
bool currCol = 0;
if (!(lb <= currReq && currReq <= rb)) currCol = 1;
string res;
for (int i = n-1; i>=0; i--) {
if (currCol) res.push_back('A');
else res.push_back('B');
currReq -= currCol;
int currVal = 0;
if (currCol) currVal = a[i];
if (!currCol) currVal = b[i];
if ((i==0?1:(currVal >= a[i-1])) && bcktrck[i][0] <= currReq && currReq <= bcktrck[i][1]) {
currCol = 1;
}
if ((i==0?1:(currVal >= a[i-1])) && bcktrck[i][2] <= currReq && currReq <= bcktrck[i][3]) {
currCol = 0;
}
}
reverse(res.begin(), res.end());
cout << res << "\n";
return 0;
}
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