Maximum Total from Optimal Activation Order

Given pairs (value[i], limit[i]), find an activation order that maximizes the sum of values where you can activate i only if the current number of active elements is strictly less than limit[i], and after each activation any items with limit ≤ the new active count become permanently unusable. The core challenge is ordering selections under changing feasibility constraints — a greedy/priority-queue style scheduling problem that balances choosing high-value items while keeping the active count low enough to enable others.