<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>

class Solution:
    def largestMultipleOfThree(self, digits: List[int]) -> str:
        
        counts = [0]*10
        for d in digits:
            counts[d] += 1
        
        total = sum((d*n for d,n in enumerate(counts)))

        def remove_dmod(counts, total, remainder):
            for d in range(10):
                if d % 3 == remainder % 3 and counts[d]:
                    counts[d] -= 1
                    total -= d
                    break
            return counts, total

        # try to remove a single digit to achieve %3=0
        if total % 3 != 0:
            counts, total = remove_dmod(counts, total, total%3)
        # we'll have to remove two of the opposing remainder
        if total % 3 == 1:
            counts, total = remove_dmod(counts, total, 2)
            counts, total = remove_dmod(counts, total, 2)
        if total % 3 == 2:
            counts, total = remove_dmod(counts, total, 1)
            counts, total = remove_dmod(counts, total, 1)

        # not possible/no digits
        if counts[0] == 0 and total == 0: return ''
        # leading zeros
        if counts[0] and total == 0: return '0'

        # construct the string
        result = ''
        for i in range(9, -1, -1):
            result += str(i)*counts[i]

        return result
        
        




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