Make Bipartite 2

AtCoder

IDabc282_d

Time2000ms

Memory256MB

Difficulty—

You are given a simple undirected graph $G$ with $N$ vertices and $M$ edges (a simple graph does not contain self-loops or multi-edges). For $i = 1, 2, \ldots, M$, the $i$\-th edge connects vertex $u_i$ and vertex $v_i$. Print the number of pairs of integers $(u, v)$ that satisfy $1 \leq u \lt v \leq N$ and both of the following conditions. * The graph $G$ does not have an edge connecting vertex $u$ and vertex $v$. * Adding an edge connecting vertex $u$ and vertex $v$ in the graph $G$ results in a bipartite graph. What is a bipartite graph?An undirected graph is said to be **bipartite** if and only if one can paint each vertex black or white to satisfy the following condition. * No edge connects vertices painted in the same color. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $0 \leq M \leq \min \lbrace 2 \times 10^5, N(N-1)/2 \rbrace$ * $1 \leq u_i, v_i \leq N$ * The graph $G$ is simple. * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $u_1$ $v_1$ $u_2$ $v_2$ $\vdots$ $u_M$ $v_M$ [samples]

Samples

Input #1

Output #1

2

We have two pairs of integers $(u, v)$ that satisfy the conditions in the problem statement: $(1, 4)$ and $(1, 5)$. Thus, you should print $2$.  
The other pairs do not satisfy the conditions. For instance, for $(1, 3)$, the graph $G$ has an edge connecting vertex $1$ and vertex $3$; for $(4, 5)$, adding an edge connecting vertex $4$ and vertex $5$ in the graph $G$ does not result in a bipartite graph.

Input #2

Output #2

0

Note that the given graph may not be bipartite or connected.

Input #3

Output #3

API Response (JSON)

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      "statement_type": "Markdown",
      "content": "You are given a simple undirected graph $G$ with $N$ vertices and $M$ edges (a simple graph does not contain self-loops or multi-edges). For $i = 1, 2, \\ldots, M$, the $i$\\-th edge connects vertex $u_...",
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