Debt Settlement

You have a group of people who have been lending money to each other, and now they need to settle all their debts. You're given a list of transactions where each transaction tells you: who paid, who received, and how much money was transferred.

Specifically, you receive an array transactions where each element transactions[i] = [from_i, to_i, amount_i] means:

• Person with ID from_i gave amount_i dollars to person with ID to_i

After all these transactions, some people might owe money while others are owed money. Your task is to find the minimum number of new transactions needed to completely settle all debts so that everyone's balance becomes zero.

For example, if person A owes $10 and person B is owed $10, they can settle with just 1 transaction (A pays B $10). But if there are multiple people with various debts and credits, finding the minimum number of transactions becomes more complex.

The key insight is that people with positive balances (those who are owed money) need to receive payments from people with negative balances (those who owe money). The challenge is to arrange these settlements in the most efficient way possible to minimize the total number of transactions.