Note: the time limit for this problem is 3s, 50% larger than the default. The memory limit is twice the default.

There are initially $M$ ($1\le M\le 2\cdot 10^5$) pairs of friends among FJ's $N$ ($2\le N\le 2\cdot 10^5$) cows labeled $1\dots N$. The cows are leaving the farm for vacation one by one. On day $i$, the $i$-th cow leaves the farm, and all pairs of the $i$-th cow's friends still present on the farm become friends. How many new friendships are formed in total?

Input Format

The first line contains $N$ and $M$.

The next $M$ lines contain two integers $u_i$ and $v_i$ denoting that cows $u_i$ and $v_i$ are friends ($1\le u_i,v_i\le N$, $u_i\neq v_i$). No unordered pair of cows appears more than once.

Output Format

One line containing the total number of new friendships formed. Do not include pairs of cows that were already friends at the beginning.

Sample Input

7 6
1 3
1 4
7 1
2 3
2 4
3 5

Sample Output

5

On day $1$, three new friendships are formed: $(3,4)$, $(3,7)$, and $(4,7)$.

On day $3$, two new friendships are formed: $(4,5)$ and $(5,7)$.

Scoring

• Test cases 2-3 satisfy $N\le 500$.
• Test cases 4-7 satisfy $N\le 10^4$.
• Test cases 8-17 satisfy no additional constraints.

Problem credits: Benjamin Qi