Input (grade 13): Cities with more than 100,000 inhabitants (and smaller towns in some states) do usually not belong to a district, but take over district responsibilities themselves, similar to the concept of independent cities.
Output (grade 9): Cities with more than 100,000 inhabitants (and smaller towns in some states) are not usually part of a district, but do the work of a district themselves. These cities belong to a district, but still do so the districts jobs themselves, as though they were independent.