<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>

def add(d, a,b,c, zero, one, two):
    if a:
        nzero = a+d
    else:
        nzero = zero
    if b:
        none = b+d
    else:
        none = one
    if c:
        ntwo = c+d
    else:
        ntwo = two

    return nzero, none, ntwo

def comparator(arr):
    return len(arr)

class Solution:
    def largestMultipleOfThree(self, digits: List[int]) -> str:
        digit_count = defaultdict(int)
        for d in digits:
            digit_count[d] += 1
        zero = ''
        one = ''
        two = ''
        for d in [9,8,7,6,5,4,3,2,1,0]:
            category = d%3
            count = digit_count[d]
            d = str(d)
            for _ in range(count):
                if category == 0:
                    nzero, none, ntwo = add(d, zero, one, two, zero, one, two)
                    if nzero == '':
                        nzero = d
                elif category == 1:
                    nzero, none, ntwo = add(d, two, zero, one, zero, one, two)
                    if none == '':
                        none = d
                else:
                    nzero, none, ntwo = add(d, one, two, zero, zero, one, two)
                    if ntwo == '':
                        ntwo = d
                zero = max(zero, nzero, key=comparator)
                one = max(one, none, key=comparator)
                two = max(two, ntwo, key=comparator)

        while len(zero) > 1 and zero[0] == '0':
            zero = zero[1:]
        return zero
        
        
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