Problem $3.(10$ points$)$ SELECTIONSORT is another algorithm for sorting numbers in an array A$[1$ : n$]$: SELECTIONSORT$($A$,$ n$)$

$1$ for i $=1$ to n $1$

$2$ minIndex $=$ i

$3$ for j $=$ i $+1$ to n

$4$ if A$[$j$]<$ A$[$minIndex $]$

$5$ minIndex $=$ j

$6$ if minIndex $=$ i

$7$ swap A$[$i$]$ with A$[$minIndex $]$

$($a$)(4$ points$)$ Show that running time of SELECTIONSORT is O$($n$2).$