<p>Given an array of digits <code>digits</code>, return <em>the largest multiple of <strong>three</strong> that can be formed by concatenating some of the given digits in <strong>any order</strong></em>. If there is no answer return an empty string.</p>

<p>Since the answer may not fit in an integer data type, return the answer as a string. Note that the returning answer must not contain unnecessary leading zeros.</p>

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

<pre>
<strong>Input:</strong> digits = [8,1,9]
<strong>Output:</strong> &quot;981&quot;
</pre>

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

<pre>
<strong>Input:</strong> digits = [8,6,7,1,0]
<strong>Output:</strong> &quot;8760&quot;
</pre>

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

<pre>
<strong>Input:</strong> digits = [1]
<strong>Output:</strong> &quot;&quot;
</pre>

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

<ul>
	<li><code>1 &lt;= digits.length &lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= digits[i] &lt;= 9</code></li>
</ul>

sys.set_int_max_str_digits(10000)
class Solution:
    def largestMultipleOfThree(self, digits: List[int]) -> str:

        digits.sort()
        digits = digits[::-1]
        mod = 0

        dp = {}

        for i in range(len(digits), -1, -1):
            for mod in [0,1,2]:
                for non_zero in [True, False]:
                    if i == len(digits):
                        dp[(i, mod, non_zero)] = "" if mod == 0 else "-1"
                        continue

                    res = "-1"
                    temp_1 = "-1"
                    
                    if non_zero or digits[i]!=0:
                        temp_1 = dp[(i+1, (mod+digits[i])%3, True)]

                    temp_2 = dp[(i+1, mod, non_zero)]
            
                    if temp_1 !="-1":
                        res = str(digits[i])+temp_1

                    if temp_2 != "-1" and res == "-1":
                        res = temp_2
                   
                    
                    elif temp_2 != "-1":
                        if len(temp_2) > len(res) or (len(temp_2) == len(res) and temp_2>=res):
                            res = temp_2
                    
                    dp[(i, mod, non_zero)] = res
                            
        
        ans = dp[(0, 0, False)]
        return "0" if ans == "" and 0 in digits else ans
            
        

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