7. (10) At a dance party there are 100 men and 30 women. For each 1' from 1, 2, . . . , 100, the ith man selects a group of ai women as potential dance partners (his \"dance list\" if you will), but in such a way that given any group of 30 men, it is always possible to pair the 30 men with the 30 women, with each man paired with a woman on his dance list. Prove that 2130 is the smallest sum a1 + a2 + . . . + (1100 for which there is a selection of dance lists that will guarantee this