<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:

        dp1 = [[0] * len(nums) for _ in range(3)]
        dp1[nums[0] % 3][0] = nums[0]

        for i in range(1, len(nums)):
            index1 = (nums[i] + dp1[0][i - 1]) % 3
            index2 = (nums[i] + dp1[1][i - 1]) % 3
            index3 = (nums[i] + dp1[2][i - 1]) % 3

            dp1[index1][i] = max(dp1[index1][i], dp1[0][i - 1] + nums[i])
            dp1[index2][i] = max(dp1[index2][i], dp1[1][i - 1] + nums[i])
            dp1[index3][i] = max(dp1[index3][i], dp1[2][i - 1] + nums[i])

            dp1[0][i] = max(dp1[0][i - 1], dp1[0][i])
            dp1[1][i] = max(dp1[1][i - 1], dp1[1][i])
            dp1[2][i] = max(dp1[2][i - 1], dp1[2][i])

        return dp1[0][len(nums) - 1]
        # grid=[[0 for i in range(len(nums))] for j in range(3)]
        # if nums[0]%3 == 0:
        #     grid[0][0]=nums[0]
        # elif nums[0]%3==1:
        #     grid[1][0]=nums[0]
        # else:
        #     grid[2][0]=nums[0]
        # for i in range(1,len(nums)):
        #     grid[0][i]=grid[0][i-1]
        #     grid[1][i]=grid[1][i-1]
        #     grid[2][i]= grid[2][i-1]
        #     a,b,c = grid[0][i-1]+nums[i],grid[1][i-1]+nums[i],grid[2][i-1]+nums[i]
        #     grid[a%3][i]=max(grid[a%3][i],a)
        #     grid[b%3][i]= max(grid[b%3][i],b)
        #     grid[c%3][i]= max(grid[c%3][i],c)
        # return grid[0][-1]
            # grid[(grid[0][i-1]+nums[i])%3][i] = max(grid[(grid[0][i-1]+nums[i])%3]+nums[i])
23600