AT_arc205_b [ARC205B] Triangle Toggle

There is a complete graph with $ N $ vertices numbered $ 1 $ to $ N $ . Each edge is colored black or white. For $ i=1,2,\ldots,M $ , the edge connecting vertices $ U_i $ and $ V_i $ is colored black, and all other edges are colored white. You can perform the following operation zero or more times. - Choose a triple of integers $ (a,b,c) $ satisfying $ 1\le a < b < c \le N $ , and repaint each of the following three edges: white to black, black to white. - The edge connecting vertices $ a $ and $ b $ - The edge connecting vertices $ b $ and $ c $ - The edge connecting vertices $ a $ and $ c $ Find the maximum number of edges that can be colored black when you perform operations appropriately.

The input is given from Standard Input in the following format: > $ N $ $ M $ $ U_1 $ $ V_1 $ $ U_2 $ $ V_2 $ $ \vdots $ $ U_M $ $ V_M $

Output the answer.

### Sample Explanation 1 By performing two operations as follows, you can make the number of black edges $ 5 $ . - Choose $ (a,b,c)=(1,3,4) $ . Then, we have the following four black edges. - The edge connecting vertices $ 1 $ and $ 2 $ - The edge connecting vertices $ 1 $ and $ 3 $ - The edge connecting vertices $ 1 $ and $ 4 $ - The edge connecting vertices $ 3 $ and $ 4 $ - Choose $ (a,b,c)=(2,3,4) $ . Then, we have the following five black edges. - The edge connecting vertices $ 1 $ and $ 2 $ - The edge connecting vertices $ 1 $ and $ 3 $ - The edge connecting vertices $ 1 $ and $ 4 $ - The edge connecting vertices $ 2 $ and $ 3 $ - The edge connecting vertices $ 2 $ and $ 4 $ You cannot make the number of black edges more than $ 5 $ , so output $ 5 $ . ### Sample Explanation 3 Be careful about overflow. ### Constraints - $ 3\le N\le 2\times 10^5 $ - $ \displaystyle 0\le M\le 2\times 10^5 $ - $ 1\le U_i < V_i \le N $ - $ (U_i , V_i) \neq (U_j , V_j) $ $ (i \neq j) $ - All input values are integers.