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A group of friends went on holiday and sometimes lent each other money. For example, Alice paid for Bill's lunch for $10. Then later Chris gave Alice $5 for a taxi ride. We can model each transaction as a tuple (x, y, z) which means person x gave person y $z. Assuming Alice, Bill, and Chris are person 0, 1, and 2 respectively (0, 1, 2 are the person's ID), the transactions can be represented as `[[0, 1, 10], [2, 0, 5]]`

.

Given a list of transactions between a group of people, return the minimum number of transactions required to settle the debt.

**Note:**

- A transaction will be given as a tuple (x, y, z). Note that
`x ≠ y`

and`z > 0`

. - Person's IDs may not be linear, e.g. we could have the persons 0, 1, 2 or we could also have the persons 0, 2, 6.

**Example 1:**

Input:[[0,1,10], [2,0,5]]Output:2Explanation:Person #0 gave person #1 $10. Person #2 gave person #0 $5. Two transactions are needed. One way to settle the debt is person #1 pays person #0 and #2 $5 each.

**Example 2:**

Input:[[0,1,10], [1,0,1], [1,2,5], [2,0,5]]Output:1Explanation:Person #0 gave person #1 $10. Person #1 gave person #0 $1. Person #1 gave person #2 $5. Person #2 gave person #0 $5. Therefore, person #1 only need to give person #0 $4, and all debt is settled.

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