<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>

from typing import List
class Solution:
    def largestMultipleOfThree(self, digits: List[int]) -> str:
        count = [0] * 10
        for digit in digits:
            count[digit] += 1
        total_sum = sum(digit * count[digit] for digit in range(10))
        remainder = total_sum % 3
        def remove_digits(remainder):
            if remainder == 1:
                for d in [1, 4, 7]:
                    if count[d] > 0:
                        count[d] -= 1
                        return True
                needed = 2
                for d in [2, 5, 8]:
                    while count[d] > 0 and needed > 0:
                        count[d] -= 1
                        needed -= 1
                    if needed == 0:
                        return True
            elif remainder == 2:
                for d in [2, 5, 8]:
                    if count[d] > 0:
                        count[d] -= 1
                        return True
                needed = 2
                for d in [1, 4, 7]:
                    while count[d] > 0 and needed > 0:
                        count[d] -= 1
                        needed -= 1
                    if needed == 0:
                        return True
            return False
        if remainder != 0:
            if not remove_digits(remainder):
                return ""  
        result = []
        for d in range(9, -1, -1):
            result.extend([str(d)] * count[d])
        if result and result[0] == '0':
            return "0"
        return ''.join(result)

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