Implement the following $3$ functions and put your code for $3$ functions in a single file called homework$2.$cpp$.$ Function $1$: int out$\_$of$\_$order$($int a$[,$int n$)$;

This function returns the number of out order pairs in an array a of size $n.$ Example $1$ : input: $a=[3,1,2],n=3$ return: $2($there are $2$ pairs that are out of order: $(3,1)$ and $(3,2))$ Example $2$: input: $a=[1,2,3,4,5],n=5$ return: $0($all pairs are in order$)$ Example $3$ : input: $a=[1,5,3,2],n=4$ return: $3($there are $3$ pairs that are out of order: $(5,3),(5,2),(3,2))$

Function $2$: string binary$\_$to$\_$hex$($const string& s$)$;

this function converts a binary string s into a hexadecimal string Example $1$: input: $s="11010"$ return: $"1$a$"$ Example $2$: input: s$="111000011111"$ return: $"$e$1$f$"$

Function $3$: void shift$\_,$ int $n)$; ${?}^{***********}$ This function shifts all $0$ to the end of array a while keeping non$-0$ numbers in the same order. Change the array a in place. Don't create a new array. Example $1$: input: $a=[1,0,2,0,3],n=5$ output: $a=[1,2,3,0,0]$ Example $2$: input: $a=[0,2,0,0,1,3],n=6$ output: $a=[2,1,3,0,0,0]$