Consider the following one$-$one matching instance with $n=5.$

$s_1$:$c_2>-c_1>-c_3>-c_4>-c_5$

$s_2$:$c_1>-c_2>-c_5>-c_3>-c_4$

$s_3$:$c_3>-c_4>-c_5>-c_2>-c_1$

$s_4$:$c_4>-c_5>-c_3>-c_1>-c_2$

$s_5$:$c_1>-c_2>-c_5>-c_3>-c_4$

$c_1$:$s_1>-s_2>-s_3>-s_4>-s_5$

$c_2$:$s_2>-s_1>-s_4>-s_5>-s_3$

$c_3$:$s_4>-s_5>-s_3>-s_2>-s_1$

$c_4$:$s_5>-s_3>-s_4>-s_1>-s_2$

$c_5$:$s_3>-s_4>-s_5>-s_1>-s_2$

Identify all colleges who can manipulate under the SPDA and explain why. Give an inconspicuous optimal manipulation for each, if any. Analogously identify all students who can manipulate under the CPDA and give an inconspicuous optimal manipulation for each, if any.