Background from Wikipedia: “Set theory is a branch of
mathematics created principally by the German mathematician
Georg Cantor at the end of the 19th century. Initially
controversial, set theory has come to play the role of a
foundational theory in modern mathematics, in the sense of a
theory invoked to justify assumptions made in mathematics
concerning the existence of mathematical objects (such as
numbers or functions) and their properties. Formal versions of
set theory also have a foundational role to play as specifying
a theoretical ideal of mathematical rigor in proofs.”
Given this importance of sets, being the basis of
mathematics, a set of eccentric theorist set off to construct a
supercomputer operating on sets instead of numbers. The initial
SetStack Alpha is under construction, and they need you to
simulate it in order to verify the operation of the
prototype.
The computer operates on a single stack of sets, which is
initially empty. After each operation, the cardinality of the
topmost set on the stack is output. The cardinality of a set
$S$ is denoted
$S$ and is the number of
elements in $S$. The
instruction set of the SetStack Alpha is PUSH, DUP, UNION, INTERSECT, and
ADD.

PUSH will push the empty set
{} on the stack.

DUP will duplicate the topmost
set (pop the stack, and then push that set on the stack
twice).

UNION will pop the stack twice
and then push the union of the two sets on the stack.

INTERSECT will pop the stack
twice and then push the intersection of the two sets on the
stack.

ADD will pop the stack twice,
add the first set to the second one, and then push the
resulting set on the stack.
For illustration purposes, assume that the topmost element
of the stack is
\[ A=\{ \{ \}
, \{ \{ \} \} \} \]
and that the next one is
\[
B=\{ \{ \} , \{ \{ \{ \} \} \} \} . \]
For these sets, we have $A=2$ and $B=2$. Then:

UNION would result in the set
{ {}, {{}}, {{{}}} }. The output is 3.

INTERSECT would result in the
set { {} }. The output is 1.

ADD would result in the set {
{}, {{{}}}, {{},{{}}} }. The output is 3.
Input
An integer $0 \le T \le
5$ on the first line gives the cardinality of the set of
test cases. The first line of each test case contains the
number of operations $0 \le N \le
2\, 000$. Then follow $N$ lines each containing one of the
five commands. It is guaranteed that the SetStack computer can
execute all the commands in the sequence without ever popping
an empty stack.
Output
For each operation specified in the input, there will be one
line of output consisting of a single integer. This integer is
the cardinality of the topmost element of the stack after the
corresponding command has executed. After each test case there
will be a line with *** (three
asterisks).
Sample Input 1 
Sample Output 1 
2
9
PUSH
DUP
ADD
PUSH
ADD
DUP
ADD
DUP
UNION
5
PUSH
PUSH
ADD
PUSH
INTERSECT

0
0
1
0
1
1
2
2
2
***
0
0
1
0
0
***
