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 <vector>
#include <iostream>
#include <algorithm>
using namespace std;
int main() {
// step #1. read input
cin.tie(0);
ios_base::sync_with_stdio(false);
int N;
cin >> N;
vector<int> X(N), Y(N), Z(N);
for (int i = 0; i < N; i++) {
cin >> X[i] >> Y[i] >> Z[i];
}
// step #2. erase from the top
vector<int> px(N), py(N), pz(N);
for (int i = 0; i < N; i++) {
px[i] = i;
py[i] = i;
pz[i] = i;
}
sort(px.begin(), px.end(), [&](int i, int j) { return X[i] < X[j]; });
sort(py.begin(), py.end(), [&](int i, int j) { return Y[i] < Y[j]; });
sort(pz.begin(), pz.end(), [&](int i, int j) { return Z[i] < Z[j]; });
vector<bool> used(N, false);
int tx = N - 1, ty = N - 1, tz = N - 1;
bool found = false;
while (tx != -1 && ty != -1 && tz != -1) {
int mx = X[px[tx]], my = Y[py[ty]], mz = Z[pz[tz]];
int cntx = 1 + (Y[px[tx]] == my ? 1 : 0) + (Z[px[tx]] == mz ? 1 : 0);
int cnty = 1 + (Z[py[ty]] == mz ? 1 : 0) + (X[py[ty]] == mx ? 1 : 0);
int cntz = 1 + (X[pz[tz]] == mx ? 1 : 0) + (Y[pz[tz]] == my ? 1 : 0);
if (cntx >= 2) {
used[px[tx]] = true;
tx--;
}
else if (cnty >= 2) {
used[py[ty]] = true;
ty--;
}
else if (cntz >= 2) {
used[pz[tz]] = true;
tz--;
}
else {
cout << mx + my + mz << endl;
found = true;
break;
}
while (tx != -1 && used[px[tx]]) tx--;
while (ty != -1 && used[py[ty]]) ty--;
while (tz != -1 && used[pz[tz]]) tz--;
}
if (!found) {
cout << -1 << endl;
}
return 0;
}
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