19 1 s 128 MB

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(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.

## Sample Input | ## Sample Output |
---|---|

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).