from collections import Counter

def reverseShuffleMerge(s):
    char_counts = Counter(s)
    required = Counter()
    for key, value in char_counts.items():
        required[key] = value // 2
    last_char = s[-1]
    char_counts[last_char] -= 1
    required[last_char] -= 1
    result = [last_char]
    for i in range(len(s)-2, -1, -1):
        char = s[i]
        char_counts[char] -= 1
        if not required[char]:
            pass
        elif (not result) or (char >= result[-1]):
            result.append(char)
            required[char] -= 1
        else:
            while result and char < result[-1] and char_counts[result[-1]] >= required[result[-1]] +1:
                old_char = result.pop(-1)
                required[old_char] += 1
            result.append(char)
            required[char] -= 1
    return "".join(result)