Desert
Description
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.
Input
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 $U_i \neq V_i$.
Output
The output contains one integer number – the answer.
Samples
5 6
1 2
2 3
3 4
4 5
5 1
2 4
20
2 3
1 2
1 2
1 2
5
Note
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.