You are given an integer array planks, where each element represents the length of a plank.

You want to build a fence consisting of planks that all have the exact same length. To construct each plank for the fence, you may:

• Use $1$ original plank from planks.

• Combine $2$ distinct original planks from planks, resulting in a plank whose length is the sum of their individual lengths.

Each original plank in planks can be used at most $1$ time.

Return the maximum number of equal length planks you can form.

Note: You do not need to use all the original planks from planks.

Constraints:

• $1 \leq$ planks.length $\leq 1000$

• $1 \leq$ planks[i] $\leq 10^9$

Input: planks = [6,6,6]-List[int]
Output: 3-int
Explanation: Each of the three original planks already has length 6, so three equal-length planks can be formed.

Input: planks = [1,2,3,4]-List[int]
Output: 2-int
Explanation: The planks of lengths 1 and 3 can be combined to form a plank of length 4, which matches the original plank of length 4, producing two equal-length planks.

Input: planks = [2,5,9]-List[int]
Output: 1-int
Explanation: No two planks or original planks can be used to form two planks of the same length, so the maximum is one.

Input: planks = [8]-List[int]
Output: 1-int
Explanation: The single original plank can be used as one fence plank.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.