<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 {
public:
    string largestMultipleOfThree(vector<int>& digits) {
        sort(digits.begin(),digits.end());
        int n = digits.size();
        int sum = 0;
        vector<int> temp1,temp2;
        for(int i=0;i<n;i++)
        {
            sum += digits[i];
            if((digits[i]%3)==1)
            {
                temp1.push_back(i);
            }
            else if((digits[i]%3)==2)
            {
                temp2.push_back(i);
            }
        }
        unordered_map<int,bool> mp;
        string result = "";
        if((sum%3)==0)
        {
            for(int i=(n-1);i>=0;i--)
            {
                result += (digits[i] + '0');
            }
        }
        else if((sum%3)==1)
        {
            if(temp1.size()==0)
            {
                int sum = 0,idx = 0;
                while(idx<temp2.size() && (sum%3)!=1)
                {
                    sum += digits[temp2[idx]];
                    mp[temp2[idx]] = true;
                    idx += 1;
                }
                if((sum%3)==2)
                {
                    return "";
                }
            }
            else
            {
                mp[temp1[0]] = true;
            }
            bool choice = false;
            for(int i=(n-1);i>=0;i--)
            {
                if(!mp[i])
                {
                    result += (digits[i] + '0');
                    choice = true;
                }
            }
            if(!choice)
            {
                return "";
            }        
        }
        else
        {
            if(temp2.size()==0)
            {
                int sum = 0,idx = 0;
                while(idx<temp1.size() && (sum%3)!=2)
                {
                    sum += digits[temp1[idx]];
                    mp[temp1[idx]] = true;
                    idx += 1;
                }
                if((sum%3)==1)
                {
                    return "";
                }
            }
            else
            {
                mp[temp2[0]] = true;
            }
            bool choice = false;
            for(int i=(n-1);i>=0;i--)
            {
                if(!mp[i])
                {
                    result += (digits[i] + '0');
                    choice = true;
                }
            } 
            if(!choice)
            {
                return "";
            }
        }
        while(result[0]=='0' && result.size()!=1)
        {
            result.erase(result.begin());
        }
        return result;
    }
};
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