Write the C language program code $.$ You are given an integer N representing the number of nodes in the graph $.$ The graph is represented

by adjacency list $.$The next N lines represent an adjacency list where first integer is node itself and

next integers are the nodes adjacent to it in ascending order $.$ The goal is to implement the following

using a Depth$-$First Search $($DFS$)$ traversal algorithm:

$$ All path$($Node$1,$Node$2)$: Print all paths from a given source to a destination vertex. Sep$-$

arate each path with a new line $,$ otherwise print $-1$ if no path exists between nodes.

NOTE $-$ paths are printed in sorted order

$$ valid tree$()$:This function checks if the given graph is a tree or not. A valid tree has the

following properties:

$($a$)$ There are no cycles $($loops$)$ in the graph.

$($b$)$ Every vertex is reachable from the root vertex.

$($c$)$ There are no isolated vertices $($vertices not connected to the rest of the graph$).$

function prints $1$ if the given graph is a tree else $-1$

Input format:

$$ The first line contains an integer N specifying the number of nodes in the graph.

$$ Next $$N$$ lines are sequence of integers where first integer is node itself and next integers in

that line are representing nodes which are adjacent to that node.

$$ Each line of input is a character from the menu list $[$a$,$t$,$x$].$

$$ Input $$a$$ calls the function All path$($Node$1,$Node$2).$

$$ Input $$t$$ calls the function valid tree$()$

$$ Input $$x$$ terminates the execution of the program.

$$ All the inputs in a line are separated by space.

Output format:

$$ A line may contain $-1$ or $1.$

$$ The output of the result of any menu is printed in a new line.

Sample Input $1$:

$6$

$0135$

$1025$

$2134$

$302$

$42$

$501$

t

a $14$

a $01$

x

Sample Output $1$ :

$-1$

$10324$

$124$

$15032$

$01$

$0321$

$051$

Sample Input $2$:

$8$

$017$

$102$

$213456$

$32$

$42$

$52$

$62$

$70$

a $67$

a $06$

t

x

Sample Output $2$ :

$62107$

$0126$

$1$