<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 collections import defaultdict

class Solution:
    def largestMultipleOfThree(self, digits: List[int]) -> str:
        digit_counts = {i: 0 for i in range(10)}
        digit_sum = 0
        for digit in digits:
            digit_counts[digit] += 1
            digit_sum += digit

        remainder_1 = [1, 4, 7, 2, 5, 8]
        remainder_2 = [2, 5, 8, 1, 4, 7]
        while(digit_sum % 3 != 0):
            for digit in remainder_1 if digit_sum % 3 == 1 else remainder_2:
                if digit_counts[digit]:
                    digit_counts[digit] -= 1
                    digit_sum -= digit
                    break

        current_selected_digits = []
        for digit in range(9, -1, -1):
            for _ in range(digit_counts[digit]):
                current_selected_digits.append(str(digit))

        number_start = len(current_selected_digits) - 1
        for i in range(len(current_selected_digits)):
            if current_selected_digits[i] != "0":
                number_start = i
                break
        if len(current_selected_digits) > 0:
            current_selected_digits = current_selected_digits[number_start:]
        return "".join(current_selected_digits)

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