def reverseShuffleMerge(s):
    from collections import Counter

    # Calculate the frequency of each character in s
    freq = Counter(s)
    
    # Calculate the required frequency for A
    required = {char: freq[char] // 2 for char in freq}
    
    # Initialize counts of used characters
    used = {char: 0 for char in freq}
    
    result = []
    # Iterate over the string in reverse order
    for char in reversed(s):
        if used[char] < required[char]:
            # Ensure that we are making the lexicographically smallest result
            while result and result[-1] > char and used[result[-1]] + freq[result[-1]] > required[result[-1]]:
                removed_char = result.pop()
                used[removed_char] -= 1

            result.append(char)
            used[char] += 1
        
        # Decrease the frequency count as we have processed this character
        freq[char] -= 1
    
    # Convert result list to a string and return
    return ''.join(result)