At a dance party there are 100 men and 20 women. for each i from 1,2, , 100, the ith man selects a group of a, women as potential dance partners (his "dance list," if you will), but in such a way that given any group of 20 men, it is always possible to pair the 20 men with the 20 women, with each man paired with a woman on his dance list. what is the smallest sum al + a2 + + awo for which there is a selection of dance lists that will guarantee this?