<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 maxSumDivThree(self, nums: List[int]) -> int:
        mod0 = []
        mod1 = []
        mod2 = []
        for _ in range(len(nums)):
            mod0.append(0)
            mod1.append(0)
            mod2.append(0)
        
        nummod = nums[0] % 3
        if nummod == 0:
            mod0[0] = nums[0]
        elif nummod == 1:
            mod1[0] = nums[0]
        else:
            mod2[0] = nums[0]

        for idx in range(1, len(nums)):
            num = nums[idx]
            nummod = num % 3
            if nummod == 0:
                if mod0[idx-1] % 3 == 0:
                    mod0[idx] = max(mod0[idx-1] + num, mod0[idx-1])
                else:
                    mod0[idx] = mod0[idx-1]
                if mod1[idx-1] % 3 == 1:
                    mod1[idx] = max(mod1[idx-1] + num, mod1[idx-1])
                else:
                    mod1[idx] = mod1[idx-1]
                if mod2[idx-1] % 3 == 2:
                    mod2[idx] = max(mod2[idx-1] + num, mod2[idx-1])
                else:
                    mod2[idx] = mod2[idx-1]
            elif nummod == 1:
                if mod2[idx-1] % 3 == 2:
                    mod0[idx] = max(mod2[idx-1] + num, mod0[idx-1])
                else:
                    mod0[idx] = mod0[idx-1]
                if mod0[idx-1] % 3 == 0:
                    mod1[idx] = max(mod0[idx-1] + num, mod1[idx-1])
                else:
                    mod1[idx] = mod1[idx-1]
                if mod1[idx-1] % 3 == 1:
                    mod2[idx] = max(mod1[idx-1] + num, mod2[idx-1])
                else:
                    mod2[idx] = mod2[idx-1]
            else:
                if mod1[idx-1] % 3 == 1:
                    mod0[idx] = max(mod1[idx-1] + num, mod0[idx-1])
                else:
                    mod0[idx] = mod0[idx-1]
                if mod2[idx-1] % 3 == 2:
                    mod1[idx] = max(mod2[idx-1] + num, mod1[idx-1])
                else:
                    mod1[idx] = mod1[idx-1]
                if mod0[idx-1] % 3 == 0:
                    mod2[idx] = max(mod0[idx-1] + num, mod2[idx-1])
                else:
                    mod2[idx] = mod2[idx-1]
            # print(mod0)
            # print(mod1)
            # print(mod2)
            # print()
            
        return max(mod0)
24600