def max_counters(n: int, a: list[int]) -> list[int]:
    counters = [0] * n
    max_counter = 0
    last_update = 0
    condition = n + 1

    for v in a:
        if v <= n:
            index = v - 1
            if counters[index] < last_update:
                counters[index] = last_update
            counters[index] += 1
            max_counter = max(counters[index], max_counter)
        if v == condition:
            last_update = max_counter

    for k, v in enumerate(counters):
        if v < last_update:
            counters[k] = last_update

    return counters