Making Friends

문제

There are initially $MM$ ($1\le M\le 2\cdot {10}^{5}1\backslash le\; M\backslash le\; 2\backslash cdot\; 10^5$) pairs of friends among FJ's $NN$ ($2\le N\le 2\cdot {10}^{5}2\backslash le\; N\backslash le\; 2\backslash cdot\; 10^5$) cows labeled $1\dots N1\backslash dots\; N$. The cows are leaving the farm for vacation one by one. On day $ii$, the $ii$-th cow leaves the farm, and all pairs of the $ii$-th cow's friends still present on the farm become friends. How many new friendships are formed in total?

입력

The first line contains $NN$ and $MM$.

The next $MM$ lines contain two integers $u_{i}u\_i$ and $v_{i}v\_i$ denoting that cows $u_{i}u\_i$ and $v_{i}v\_i$ are friends ($1\le u_i,v_i\le N1\backslash le\; u\_i,v\_i\backslash le\; N$, $u_i\mathrm{\ne }{v}_{i}u\_i\backslash neq\; v\_i$). No unordered pair of cows appears more than once.

출력

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

힌트

On day $11$, three new friendships are formed: $(3,4)(3,4)$, $(3,7)(3,7)$, and $(4,7)(4,7)$.

On day $33$, two new friendships are formed: $(4,5)(4,5)$ and $(5,7)(5,7)$.

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

5