#include #include #include #include #include #include #include #include #define rep(i, a, b) for (int i = int(a); i < int(b); i++) using namespace std; using ll = long long int; // NOLINT using P = pair; // clang-format off #ifdef _DEBUG_ #define dump(...) do{ cerr << __LINE__ << ":\t" << #__VA_ARGS__ << " = "; debug_print(__VA_ARGS__); } while(false) template void debug_print(const T &t, const Ts &...ts) { cerr << t; ((cerr << ", " << ts), ...); cerr << endl; } #else #define dump(...) do{ } while(false) #endif template vector make_v(size_t a, T b) { return vector(a, b); } template auto make_v(size_t a, Ts... ts) { return vector(a, make_v(ts...)); } template bool chmin(T &a, const T& b) { if (a > b) {a = b; return true; } return false; } template bool chmax(T &a, const T& b) { if (a < b) {a = b; return true; } return false; } template void print(const T& t, const Ts&... ts) { cout << t; ((cout << ' ' << ts), ...); cout << '\n'; } template void input(Ts&... ts) { (cin >> ... >> ts); } template istream &operator,(istream &in, T &t) { return in >> t; } struct Inf { template constexpr operator T() { return numeric_limits::max() / 2; } }; // clang-format on #include template class FlatVector : public vector { private: array args; public: template FlatVector(F &&init, Index... arg) : vector((arg * ...), forward(init)), args({static_cast(arg)...}) {} T &idx(Index... arg) { array _args = {static_cast(arg)...}; size_t index = 0; for (size_t i = 0; i < sizeof...(Index); i++) { index *= args[i]; index += _args[i]; } return this->operator[](index); } }; template FlatVector(T, Index...) -> FlatVector; int main() { cin.tie(nullptr); ios::sync_with_stdio(false); int n; cin, n; vector> v(n); rep(i, 0, n) { int a, b, c; cin, a, b, c; v[i] = {a, b, c}; } const int bits = 1 << n; auto dp = FlatVector(0LL, bits, n, 3); ll ans = 0; rep(i, 0, n) { rep(j, 0, 3) { dp.idx(1 << i, i, j) = v[i][j]; chmax(ans, v[i][j]); } } rep(bit, 1, bits) { rep(i, 0, n) { if (!((bit >> i) & 1)) continue; rep(j, 0, 3) { ll box1, box2; if (j == 0) { box1 = v[i][1]; box2 = v[i][2]; } else if (j == 1) { box1 = v[i][0]; box2 = v[i][2]; } else { box1 = v[i][0]; box2 = v[i][1]; } if (box1 > box2) swap(box1, box2); rep(k, 0, n) { if ((bit >> k) & 1) continue; rep(l, 0, 3) { ll nbox1, nbox2; if (l == 0) { nbox1 = v[k][1]; nbox2 = v[k][2]; } else if (l == 1) { nbox1 = v[k][0]; nbox2 = v[k][2]; } else { nbox1 = v[k][0]; nbox2 = v[k][1]; } if (nbox1 > nbox2) swap(nbox1, nbox2); if (nbox1 <= box1 && nbox2 <= box2) { chmax(dp.idx(bit | (1 << k), k, l), dp.idx(bit, i, j) + v[k][l]); chmax(ans, dp.idx(bit | (1 << k), k, l)); } } } } } } print(ans); return 0; }