In the Longest$-$Common$-$Subsequence problem, the following algorithm was proposed to come up with two matrices $b$ and $c$ which contain information that allows one to identify the solution:

If $x="$s p a n k in g$"$ and $Y="$a $mp$ u t a t i $on"$ the algorithm would produce the following $c$ matrix:

With the missing $33$ matrix entries at the lower right corner of the matrix determined elsewhere in this assessment, what is the LCS for the two given sequences?

ki n $g$

p $1$ a $n$

pain

p a $n$

spain