function maxCounters(int $n, array $a): array
{
    $counters   = array_fill(0, $n, 0);
    $maxCounter = 0;
    $lastUpdate = 0;
    $condition  = $n + 1;

    foreach ($a as $v) {
        if ($v <= $n) {
            $index = $v - 1;
            if ($counters[$index] < $lastUpdate) {
                $counters[$index] = $lastUpdate; // should already be maxed
            }
            $counters[$index]++;
            $maxCounter = $counters[$index] > $maxCounter ? $counters[$index] : $maxCounter;
        }
        if ($v === $condition) {
            $lastUpdate = $maxCounter;
        }
    }

    // apply all max operations to avoid O(M*N) complexity
    foreach ($counters as $k => $v) {
        if ($v < $lastUpdate) {
            $counters[$k] = $lastUpdate;
        }
    }

    return $counters;
}