Rasmus and his friends are on vacation in Italy. Since they are suffering from the heat, they decide
to buy some ice cream. There are N flavors of ice cream available; flavors are numbered from 1 to
N. However, some pairings of flavors should be avoided; otherwise, the taste would be unpleasant.
Rasmus wants to know how many ways there are to choose three different flavors without any such
impossible pairing. The order of flavors is not taken into account.
The first line of input contains two non-negative integers N and M, the number of flavors and the
number of impossible pairings. Each of the M following lines describes an impossible pairing and
contains two different flavor numbers. No impossible pairing will appear twice.
1 ≦ N ≦ 200
0 ≦ M ≦ 10000
The first and only line of output must contain a single integer: the number of possible choices.
5 3 1 2 3 4 1 3
3
There are 5 flavors and 3 impossible pairings. Flavor 1 should be combined with neither flavor 2 nor
flavor 3, and flavor 3 also should not be chosen together with flavor 4. Only 3 ways to choose three
different flavors remain: (1 4 5), (2 3 5), and (2 4 5).
Migrated from old NTUJ.
BOI2011 Competition Day 1
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