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.
The ﬁrst line of input contains two non-negative integers N and M(1≤N≤200,0≤M≤10,000), 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.
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
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).