$(1)$ Here is the pseudocode for Hoare's partition scheme for the quicksort. PARTITION$($A$,$ lo$,$ hi$)$

$$ pivot $=$ A$[$lo$]$ i $=$ lo$-1$ j $=$ hi $+1$ while True

$$do i$=$i$+1$ while A$[$i$]<$ pivot$$ do j$=$j$-1$ while A$[$j$]>$ pivot$$ if i $>=$ j: return j$$ swap A$[$i$]$ and A$[$j$]$

This PARTITION$($A$,$ lo$,$ hi$)$ procedure inputs an array A$,$ and takes the first element x $=$ A$[$lo$]$ as the pivot element. The output is an array where all elements to the left of x are less than x$,$ and all elements to the right of x are greater than x$.$ Let A $=[1,2,7,8,9,6,3,4,5]$ and the first partition is called as PARTITION$($A$,0,$ length$($A$)-1).$ Show the array A$,$ after the first partition.