Problem Statement

You are given an array nums consisting of positive integers.

You can perform below two operations on the array multiple times:

• Select two elements with equal values and delete them from the array.
• Select three elements with equal values and delete them from the array.

Return the minimum number of operations required to make the array empty, or -1 if it is not possible.

Examples

Example 1:

• Input: nums = [1, 3, 2, 1, 2, 2, 3]
• Expected Output: 3
• Justification: We can perform the following operations:
  • Remove the two 1s (one operation).
  • Remove the three 2s (second operation).
  • Remove the two 3s (third operation). Thus, the array can be emptied in 3 operations.

Example 2:

• Input: nums = [4, 4, 2, 5, 3, 2, 5, 3]
• Expected Output: 4
• Justification: We can perform operations such as removing pairs of 4, 2, 5, and 3 in successive steps, each taking one step. This results in the array being emptied in 4 operations.

Example 3:

• Input: nums = [7, 8, 7]
• Expected Output: -1
• Justification: It is not possible to make the array empty as we can't remove 8 by performing any of 2 operations.

Try it yourself

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