<p>Given an integer array <code>nums</code>, return <em>the <strong>maximum possible sum </strong>of elements of the array such that it is divisible by three</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,6,5,1,8]
<strong>Output:</strong> 18
<strong>Explanation:</strong> Pick numbers 3, 6, 1 and 8 their sum is 18 (maximum sum divisible by 3).</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [4]
<strong>Output:</strong> 0
<strong>Explanation:</strong> Since 4 is not divisible by 3, do not pick any number.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4,4]
<strong>Output:</strong> 12
<strong>Explanation:</strong> Pick numbers 1, 3, 4 and 4 their sum is 12 (maximum sum divisible by 3).
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 4 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def Max(self, a, b):
        if a and b:
            return max(a,b)
        elif a:
            return a
        else:
            return b
    def maxSumDivThree(self, nums: List[int]) -> int:
        res = []
        n = len(nums)
        if n == 0:
            return 0
        for i in range(n):
            res.append([None]*3)

        for i in range(n):
            res[i][nums[i]%3] = nums[i]

        print(res)
        for i in range(1,n):
            cur = nums[i]
            cur_remain = cur%3
            res[i] = [self.Max(res[i][t],res[i-1][t]) for t in range(3)]
            print(f"process {cur}")
            #res[i][cur_remain] = max()
            for prev_remain in range(3):
                new_remain = (cur_remain+prev_remain) % 3
                #print(f"cur_remain={cur_remain}, prev_rem={prev_remain}, new_remain={new_remain}")
                combined = res[i-1][prev_remain]+cur if res[i-1][prev_remain] else None
                res[i][new_remain] = self.Max(combined, res[i][new_remain])
            print(f"res[{i}] = {res[i]}")

        print(res)
        return res[-1][0] if res[-1][0] else 0

        
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