P3513 [POI 2011] KON-Conspiracy

Hostile Bitotia launched a sneak attack on Byteotia and occupied a significant part of its territory. The King of Byteotia, Byteasar, intends to organise resistance movement in the occupied area. Byteasar naturally started with selecting the people who will form the skeleton of the movement. They are to be partitioned into two groups: the conspirators who will operate directly in the occupied territory, and the support group that will operate inside free Byteotia. There is however one issue - the partition has to satisfy the following conditions: Every pair of people from the support group have to know each other - this will make the whole group cooperative and efficient. The conspirators must not know each other. None of the groups may be empty, i.e., there has to be at least one conspirator and at least one person in the support group. Byteasar wonders how many ways there are of partitioning selected people into the two groups. And most of all, whether such partition is possible at all. As he has absolutely no idea how to approach this problem, he asks you for help.

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