Drop, Then Multiply

Medium

You get an integer array values. For any three indices i < j < k, the value of the triple is (values[i] - values[j]) * values[k]. Return the largest value over all such triples. If every triple has a negative value, return 0.

Example 1

values=[9, 4, 2, 5, 3] → 35

The index triple (0, 2, 3) gives (9 − 2) · 5 = 35, and nothing beats it.

Example 2

values=[2, 4, 8] → 0

The only triple gives (2 − 4) · 8 = −16 < 0, so the answer is 0.

Example 3

values=[6, 1, 10, 1, 7] → 63

Constraints

3 ≤ len(values) ≤ 10⁵
1 ≤ values[i] ≤ 10⁶

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Input

values=[9, 4, 2, 5, 3]

Expected

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