$(10$ points$)$

Among the following permutations with integers $1$ through $5,$ choose all permutations that can not

be produced by a stack under the assumption that the numbers are inserted in an increasing order $($i$.$e$.$

the sequence of $[1,2,3,4,5].$ Note that the numbers can be popped out of the stack arbitrarily.

$($a$)12345$

$($b$)32514$

$($c$)54321$

$($d$)21345$

$($e$)42135$

$($f$)12543$

$($g$)54123$

$($h$)13524$

$($i$)12354$

$($j$)13542$