Don’t be cycle

AtCoder

IDabc288_c

Time2000ms

Memory256MB

Difficulty—

You are given a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the $i$\-th edge connects vertex $A_i$ and vertex $B_i$. Let us delete zero or more edges to remove cycles from the graph. Find the minimum number of edges that must be deleted for this purpose. What is a simple undirected graph? **A simple undirected graph** is a graph without self-loops or multi-edges whose edges have no direction. What is a cycle? A **cycle** in a simple undirected graph is a sequence of vertices $(v_0, v_1, \ldots, v_{n-1})$ of length at least $3$ satisfying $v_i \neq v_j$ if $i \neq j$ such that for each $0 \leq i < n$, there is an edge between $v_i$ and $v_{i+1 \bmod n}$. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $0 \leq M \leq 2 \times 10^5$ * $1 \leq A_i, B_i \leq N$ * The given graph is simple. * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $A_2$ $B_2$ $\vdots$ $A_M$ $B_M$ [samples]

Samples

Input #1

Output #1

2

One way to remove cycles from the graph is to delete the two edges between vertex $1$ and vertex $2$ and between vertex $4$ and vertex $5$.  
There is no way to remove cycles from the graph by deleting one or fewer edges, so you should print $2$.

Input #2

4 2
1 2
3 4

Output #2

Input #3

Output #3

API Response (JSON)

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