This question is related to disjoint set operations. Assume that we are using union by rank and find$-$set with path compression. The state of a disjoint set data structure is given as follow.

$A[1]=-3,$

$A[2]=1,$

$A[3]=1,$

$A[4]=3,$

$A[5]=1,$

$A[6]=5,$

$A[7]=5,$

$A[8]=7,$

$A[9]=-3,$

$A[10]=9,$

$A[11]=9,$

$A[12]=11,$

$A[13]=9,$

$A[14]=13,$

$A[15]=13,$

$A[16]=15$

After union $(8,14),$ what is the value of $A[1],$ A$[8],$ A$[9],$ A$[14]?$