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EICONP4 - Convert Graph Into Tree

Given an undirected graph with n vertices and m edges. Vertices are numbered from 0 to n-1. Write a program to calculate the minimum total number of edges should be removed and added to convert the given graph into a tree.

Input

The first line contains the number of vertices n (1 ≤ n ≤ 105), the number of edges m (1 ≤ m ≤ 2x105).

Each of the next m lines contains 2 integers u, v representing an edge between u and v (0 ≤ u,v ≤ n).

Output

Print out the total number of removed and added edges.

Sample

Input

Output

6 5

0 1

0 2

1 3

3 1

3 4

2


Added by:Ha Minh Ngoc
Date:2022-12-25
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
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