1. Separate triplets with $$$a_i \le c_i$$$ from $$$a_i \gt c_i$$$
2. The first group is sorted in ascending order using value $$$a_i + b_i$$$ for comparing.
3. The second group is sorted in descending order using value $$$b_i + c_i$$$ for comparing.
4. Append second group to the first one.

int sign(int x) { return x < 0 ? -1 : x > 0; }
struct info_t {
  int a, b, c, id;
  int get() const {
    if (a <= c) {
      return (a + b);
    } else {
      return -(b + c);
    }
  }
  bool operator <(const info_t &y) const {
    int xg = this->get(), yg = y.get();
    if (sgn(xg) != sgn(yg)) {
      return sgn(xg) > sgn(yg);
    } else {
      return xg < yg;
    }
  }
};

int64_t ta = 0, tb = 0, tc = 0;
for (const info_t &toy : toys) {
  ta += toy.a;
  tb = max(ta, tb) + toy.b;
  tc = max(tb, tc) + toy.c;
}
// output tc