class Solution:
    def largestPalindromic(self, num: str) -> str:
        
        # count the frequencies of the numbers from 9 - 0 in a map 
        def build_counter():
            counter = {str(i): 0 for i in range(10)}
            for n in num:
                counter[n] += 1
            return counter
        
        counter = build_counter()
        
        remain = 0 # store the largest remaining number
        first_half = [] # store the first left half of the result
        result = [] # for the entire result 

        # loop for all the number from 9 to 0 in decreasing order 
        for i in range(9,0, -1):
            div = counter[str(i)] // 2 # take the division result
            rem = counter[str(i)] % 2  # the remaining 
            
            # repeat i based on it's frequency divided by 2 
            for j in range(int(div)):
                first_half.append(str(i)) 

            # find the largest remaining number if any 
            if rem == 1:
                remain = max(remain, i)
        
        # now we compose the result 
        result = first_half[:]

        # add the remain if any in the middle
        if remain > 0:
            result.append(str(remain))

        # construct the right half as reverse of of the left half
        first_half.reverse()
        for char in first_half:
            result.append(str(char))
        
        return "".join(result) if result else "0"