func maxCounters(n int, a []int) []int {
	counters := make([]int, n)
	maxCounter := 0
	lastUpdate := 0
	condition := n + 1

	for _, v := range a {
		if v <= n {
			index := v - 1
			if counters[index] < lastUpdate {
				counters[index] = lastUpdate // should already be maxed
			}
			counters[index]++
			if counters[index] > maxCounter {
				maxCounter = counters[index]
			}
		}
		if v == condition {
			lastUpdate = maxCounter
		}
	}

	// apply all max operations to avoid O(M*N) complexity
	for k, v := range counters {
		if v < lastUpdate {
			counters[k] = lastUpdate
		}
	}

	return counters
}