At a dance party there are 100 men and 20 women. For each i from 1,2, .

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 "dancelist," if you will), but in such a way that given any group of 20 men, it is alwayspossible 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 a1 + a2 + ... + a100 for which there is a selection of dance lists that will guarantee this?