Stepan and his friends went on holiday to Uzhlyandiya. While hiding from the heat, they decided to buy an ice cream. There exist n flavors of ice cream, numbered from 1 to n. Some tastes are incompatible, such couples should be avoided, otherwise it will be very unpleasant taste. Stepan wants to know the number of ways to choose three different flavors of ice cream so that among them there was no incompatible pair. The order of flavors in triples does not matter.

Input

The first line contains two nonnegative integers n and m (1 ≤ n ≤ 200, 1 ≤ m ≤ 10000) - the number of flavors and number of inconsistent pairs of flavors. Next m lines describe the pairs of incompatible flavors.

Output

Print one number - the number of ways to make a choice.

Explanation:

Possible triples are: (1 4 5), (2 3 5) и (2 4 5).