A14585. Desert

You are given an undirected graph of $N$ nodes and $M$ edges, $E_1, E_2, \dots E_M$ .

A connected graph is a cactus if each of it's edges belogs to at most one simple cycle. A graph is a desert if each of it's connected components is a cactus.

Find the number of pairs $(L, R)$ , ( $1 \leq L \leq R \leq M$ ) such that, if we delete all the edges except for $E_L, E_{L+1}, \dots E_R$ , the graph is a desert.

The first line contains two integers $N$ and $M$ ( $2 \leq N \leq 2.5 \times 10^5$ , $1 \leq M \leq 5 \times 10^5$ ). Each of the next $M$ lines contains two integers. The $i$ -th line describes the $i$ -th edge. It contains integers $U_i$ and $V_i$ , the nodes connected by the $i$ -th edge ( $E_i=(U_i, V_i)$ ). It is guaranteed that $1 \leq U_i, V_i \leq N$ and $U_i \neq V_i$ .

The output contains one integer number – the answer.

In the second example: Graphs for pairs $(1, 1)$ , $(2, 2)$ and $(3, 3)$ are deserts because they don't have any cycles. Graphs for pairs $(1, 2)$ and $(2, 3)$ have one cycle of length 2 so they are deserts.