## Description

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 inmathematics
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 Set-
Stack 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 <= T <= 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 <= N <= 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

2
9
PUSH
DUP
ADD
PUSH
ADD
DUP
ADD
DUP
UNION
5
PUSH
PUSH
ADD
PUSH
INTERSECT

## Sample Output

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

## Source

nwerc 2006