<p>You are given a string <code>num</code> consisting of digits only.</p>

<p>Return <em>the <strong>largest palindromic</strong> integer (in the form of a string) that can be formed using digits taken from </em><code>num</code>. It should not contain <strong>leading zeroes</strong>.</p>

<p><strong>Notes:</strong></p>

<ul>
	<li>You do <strong>not</strong> need to use all the digits of <code>num</code>, but you must use <strong>at least</strong> one digit.</li>
	<li>The digits can be reordered.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;444947137&quot;
<strong>Output:</strong> &quot;7449447&quot;
<strong>Explanation:</strong> 
Use the digits &quot;4449477&quot; from &quot;<u><strong>44494</strong></u><u><strong>7</strong></u>13<u><strong>7</strong></u>&quot; to form the palindromic integer &quot;7449447&quot;.
It can be shown that &quot;7449447&quot; is the largest palindromic integer that can be formed.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;00009&quot;
<strong>Output:</strong> &quot;9&quot;
<strong>Explanation:</strong> 
It can be shown that &quot;9&quot; is the largest palindromic integer that can be formed.
Note that the integer returned should not contain leading zeroes.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= num.length &lt;= 10<sup>5</sup></code></li>
	<li><code>num</code> consists of digits.</li>
</ul>

class Solution:
    def largestPalindromic(self, num: str) -> str:
        # make counter
        counts = {}
        for digit in num:
            if digit not in counts:
                counts[digit] = 0
            counts[digit] += 1
        odd_digits = []
        num_in_result = {}
        for digit in counts:
            if counts[digit] > 1:
                num_in_result[digit] = counts[digit] // 2
            if counts[digit] % 2 == 1:
                odd_digits.append(digit)
        
        half_result = ''
        sorted_keys = list(num_in_result.keys())
        sorted_keys.sort(reverse=True)
        if sorted_keys and sorted_keys[0] != '0':
            for digit in sorted_keys:
                for _ in range(num_in_result[digit]):
                    half_result += digit
        half_len = len(half_result)
        result = half_result
        if odd_digits:
            result += max(odd_digits)
        for i in range(half_len):
            result += half_result[-i-1]
        if not result:
            return '0'
        return result
            

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