Write the program in C language code. You are given a sequence of operations to perform on an AVL tree. Each operation is represented

by a character followed by its respective parameters. The operations are as follows: $[$i $,$x $,$p $,$s $,$

e$]$

Input format:

$$Each line contains a character from $$i$,$x$,$p$,$s$,$e$$followed by zero or one integers. The

integers, if given, are in the range in $[1,106].$

$$i: AVL insert$($T$,$key$)-$Insert the given key into the AVL tree T$.$

$$x: AVL find$($T$,$key$)-$Search for the given key in the AVL tree T$.$If the key is found, print

the path from the root to the node containing the key; otherwise, print $-1.$

$$p: AVL preorder$($T$)-$Print the preorder traversal of the AVL tree T$.$

$$s: AVL cal$($T$)-$Given a point, calculate the total number of left and right rotations required

to balance the AVL tree T at that point. left rotation, right rotation separated by space

$$e: Exit $-$Terminate the sequence of operations.

NOTE : key in $[1,106]$

Output format:

For

$$x : sequence of integers with space separated them representing path

$$p : sequence of integers with space separated them representing preorder.

$$s : two integer representing total number of left rotaions and right rotaions

Sample Input $1$:

$4$

i $10$

i $20$

i $30$

s

i $40$

p

i $50$

i$5$

i$1$

s

x $10$

x $56$

e

Sample Output $1$:

$10$

$20103040$

$21$

$20510$

$-1$

Sample Input $2$:

i $167$

i $34$

i $121$

s

i $56$

i $198$

i $73$

i $112$

p

x $112$

s

e

Sample Output $2$:

$11$

$121563473112167198$

$1215673112$

$21$