Problem Statement

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.

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.

Input

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

Output the answer.