from collections import Counter

def reverseShuffleMerge(s):
    # find character frequencies in the desired string A
    freq = {key: val // 2 for key, val in Counter(s).items()}

    # repeat gready approach until solution is complete
    solution = []
    n = len(s)
    while len(solution) < n // 2:
        left_freq = Counter(s)
        next_char = {}
        min_char = '~'
        # search original string S backwards
        for index in range(len(s)-1, -1, -1):
            char = s[index]
            # it is possible to take this char as the next one
            if char not in next_char and freq[char] > 0:
                next_char[char] = index
                min_char = min(min_char, char)
            # there's not enough letters available to the left
            left_freq[char] -= 1
            if left_freq[char] < freq[char]:
                break
        # add minimal char as the next one (greedy)
        solution += min_char
        freq[min_char] -= 1
        s = s[0:next_char[min_char]]

    return "".join(solution)