Question $3$: DES $(50$ points$)$

Use java. Please implement the formal F$-$function in DES. There should be two inputs Ri and Ki$.$ Given Ri $($the right part of the block$)$ and Ki $($the round key$)$ of each round in the DES, please figure out what the output is $($after permutation step$).$

Test cases:

Inputs: Ri $="$A$1$B$2$C$3$D$4",$ Ki $="$F$0$D$532$A$490$C$6"$

Output: $18959$CF$7$

Here are some tables you can use for this question.

Expansion box:

$\{$

$32,1,2,3,4,5,$

$4,5,6,7,8,9,$

$8,9,10,11,12,13,$

$12,13,14,15,16,17,$

$16,17,18,19,20,21,$

$20,21,22,23,24,25,$

$24,25,26,27,28,29,$

$28,29,30,31,32,1$

$\}$;

Permutation box:

$\{$

$16,7,20,21,$

$29,12,28,17,$

$1,15,23,26,$

$5,18,31,10,$

$2,8,24,14,$

$32,27,3,9,$

$19,13,30,6,$

$22,11,4,25$

$\}$;

$8$ substitution boxes:

sbox $=[[[14,4,13,1,2,15,11,8,3,10,6,12,5,9,0,7],$

$[0,15,7,4,14,2,13,1,10,6,12,11,9,5,3,8],$

$[4,1,14,8,13,6,2,11,15,12,9,7,3,10,5,0],$

$[15,12,8,2,4,9,1,7,5,11,3,14,10,0,6,13]],$

$[[15,1,8,14,6,11,3,4,9,7,2,13,12,0,5,10],$

$[3,13,4,7,15,2,8,14,12,0,1,10,6,9,11,5],$

$[0,14,7,11,10,4,13,1,5,8,12,6,9,3,2,15],$

$[13,8,10,1,3,15,4,2,11,6,7,12,0,5,14,9]],$

$[[10,0,9,14,6,3,15,5,1,13,12,7,11,4,2,8],$

$[13,7,0,9,3,4,6,10,2,8,5,14,12,11,15,1],$

$[13,6,4,9,8,15,3,0,11,1,2,12,5,10,14,7],$

$[1,10,13,0,6,9,8,7,4,15,14,3,11,5,2,12]],$

$[[7,13,14,3,0,6,9,10,1,2,8,5,11,12,4,15],$

$[13,8,11,5,6,15,0,3,4,7,2,12,1,10,14,9],$

$[10,6,9,0,12,11,7,13,15,1,3,14,5,2,8,4],$

$[3,15,0,6,10,1,13,8,9,4,5,11,12,7,2,14]],$

$[[2,12,4,1,7,10,11,6,8,5,3,15,13,0,14,9],$

$[14,11,2,12,4,7,13,1,5,0,15,10,3,9,8,6],$

$[4,2,1,11,10,13,7,8,15,9,12,5,6,3,0,14],$

$[11,8,12,7,1,14,2,13,6,15,0,9,10,4,5,3]],$

$[[12,1,10,15,9,2,6,8,0,13,3,4,14,7,5,11],$

$[10,15,4,2,$

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