<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:
        # examples: 7, 2, 1
        # 8, 2, 1 <- total=11, 11%3=2
        # 7, 2, 1, 1
        # 9, 4 <- total=13, 13%3=1
        # 6, 4, 1, 1, 1 <- total=13, 13%3=1
        # three cases: total%3 equals 0 or 1 or 2 <- good for total%3=0
        # case total%3=1: remove 1 or 4<-(2+2 or 4) or 7<-(2+5 or 7) or 10<-(5+5 or 2+8)
        #                             13<-(5+8) or 16<-(8+8)
        # case total%3=2: remove 2<-(1+1 or 2) or 5<-(1+4 or 5) or 8<-(4+4 or 1+7 or 8)
        #                             11<-(4+7) or 14<-(7+7)
        # 9 4 2 2

        count = [0]*10
        for digit in digits:
            count[digit] += 1
        total = sum(digits)
        toremove = total%3

        if toremove==1:
            # following cases
            if count[1]>0:
                count[1] -= 1
            elif count[4]>0:
                count[4] -= 1
            elif count[7]>0:
                count[7] -= 1
            elif count[2]>1:
                count[2] -= 2
            elif count[2]>0 and count[5]>0:
                count[2] -= 1
                count[5] -= 1
            elif count[5]>1:
                count[5] -= 2
            elif count[2]>0 and count[8]>0:
                count[2] -= 1
                count[8] -= 1
            elif count[5]>0 and count[8]>0:
                count[5] -= 1
                count[8] -= 1
            elif count[8]>1:
                count[8] -= 2
            else:
                return ""

        if toremove==2:
            if count[2]>0:
                count[2] -= 1
            elif count[5]>0:
                count[5] -= 1
            elif count[8]>0:
                count[8] -= 1
            elif count[1]>1:
                count[1] -= 2
            elif count[1]>0 and count[4]>0:
                count[1] -= 1
                count[4] -= 1
            elif count[4]>1:
                count[4] -= 2
            elif count[1]>0 and count[7]>0:
                count[1] -= 1
                count[7] -= 1
            elif count[4]>0 and count[7]>0:
                count[4] -= 1
                count[7] -= 1
            elif count[7]>1:
                count[7] -= 2
            else:
                return ""

        result = "".join([str(i)*count[i] for i in range(9, -1, -1)])
        if result and result[0]=="0":
            return "0"
        return result
# TC: O(N)
# SC: O(1)
124