[智商测试]condem problem

genghis

M boys and N girls decide to hold a sex party in which any
two of them with opposing sex will have sex once and only once. They want to
consume as least as possible condoms while ensuring safe sex. By the term
"safe sex" they want to make sure that
1. the inside of any condom can touch at most one boy;
2. the outside of any condom can touch at most one girl;
3. two or more condoms can be used together when one is fit into another.
however, if the outside of the inner condom has been contaminated, then by
touching with it the outer condom's inside gets contaminated too. similary, if
the inside of the outer condom has been contaminated, then by touching with it,
the outside of the inner condom gets contaminated.A contaminated side should
never touch anybody else again except the one who caused that contamination;
4. condoms can be repeatedly used.
Find out the mimimum number of condoms required.