<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:
        pending_counter = collections.Counter(digits)
        sum_of_digits = sum(digits)

        def remove_digits(counter, remainder):
            if counter[remainder] + counter[remainder + 3] + counter[remainder + 6] > 0:
                while True:
                    if counter[remainder] > 0:
                        counter[remainder] -= 1
                        break
                    remainder += 3
                return True
            else:
                remainder = 3 - remainder
                if counter[remainder] + counter[remainder + 3] + counter[remainder + 6] > 1:
                    digits_removed = 2
                    while digits_removed > 0:
                        if counter[remainder] > 0:
                            counter[remainder] -= 1
                            digits_removed -= 1
                            continue
                        remainder += 3
                    return True
                return False
        
        remainder = sum_of_digits % 3
        if remainder != 0:
            if not remove_digits(pending_counter, remainder):
                return ""
        
        ans = ""
        for i in range(9, -1, -1):
            while pending_counter[i] > 0:
                ans += str(i)
                pending_counter[i] -= 1
        
        if len(ans) == 0:
            return ans
        elif ans[0] == '0':
            return "0"
        else:
            return ans

        

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