There are $2*$ N nodes in an undirected graph, and a number of edges connecting some nodes. In each edge, the first value will be between $1$ and N$,$ inclusive. The second node will be between N $+1$ and $,2*$ N inclusive. Given a list of edges, determine the size of the smallest and largest connected components that have or more nodes. A node can have any number of connections. The highest node value will always be connected to at least $1$ other node.

Note Single nodes should not be considered in the answer.

Function Description

Complete the connectedComponents function in the editor below.

connectedComponents has the following parameter$($s$)$:

$-$ int bg$[$n$][2]$: a $2-$d array of integers that represent node ends of graph edges

Returns

$-$ int$[2]$: an array with $2$ integers, the smallest and largest component sizes

Input Format

The first line contains an integer n$,$ the size of bg$.$

Each of the next n lines contain two space$-$separated integers, bg$[$ i $][0]$ and $.$ bg$[$ i $][1]$