<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:
        total = sum(digits)
        digits.sort(reverse=True)
        if total%3==0: 
            if not digits: return ""
            if digits[0] == 0: return "0"
            return "".join(map(str,digits))
        elif total%3==1:
            removed = [{1:1},{4:1},{7:1},{2:2},{2:1,5:1},{2:1,8:1},{5:2},{5:1,8:1},{8:2}]
            for term in removed:
                can = True
                for key in term:
                    if key not in digits or digits.count(key) < term[key]:
                        can = False
                        break
                if can:
                    for key in term:
                        for i in range(term[key]):
                            digits.remove(key)
                    if not digits: return ""
                    if digits[0] == 0: return "0"
                    return "".join(map(str,digits))
        else:
            removed = [{2:1},{5:1},{8:1},{1:2},{1:1,4:1},{1:1,7:1},{4:2},{4:1,7:1},{7:2}]
            for term in removed:
                can = True
                for key in term:
                    if key not in digits or digits.count(key) < term[key]:
                        can = False
                        break
                if can:
                    for key in term:
                        for i in range(term[key]):
                            digits.remove(key)
                    if not digits: return ""
                    if digits[0] == 0: return "0"
                    return "".join(map(str,digits))
        return ""

                
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