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You do not need to read the Interleaved Output: Part 2 problem to be able to solve this problem. Both Part 1 and Part 2 have the same first two paragraphs (not including this informational text). We have underlined the critical difference between the two parts.
On a distant moon of Jupiter, some developer conference events are about to happen! They are called
IO (uppercase I, uppercase O),
Io (uppercase I, lowercase o),
iO (lowercase I, uppercase O), and
io (lowercase I, lowercase O).
The best way to advertise an event is by using special computers that print the event's name one character at a time, with the output appearing on a digital display. Each such computer only knows the name of one event, and is programmed to print its event's name zero or more times. For example, a computer programmed to print
IO twice prints an
I, followed by an
O, followed by an
I, followed by an
O, for a final string of
You know that the conference organizers are using these computers, but you do not know how many computers are advertising each event. For each event, there may be any number of computers (including zero) programmed to print the event's name. Moreover, the computers are not necessarily all programmed to print the same number of times. For example, it is possible that there are three computers programmed to print
Io once each, and one computer programmed to print
The computers have all finished printing, but unfortunately, they all printed to the same display! Because the computers printed concurrently, event names in the final output string may be interleaved. You are considering the possible ways in which that string could have been produced.
For example, the string
IiOioIoO could have been produced by two computers, as follows:
index: 1 2 3 4 5 6 7 8 A: I . . . o I o . B: . i O i . . . O string: I i O i o I o O
In this interpretation, the
Io event was advertised twice, the
iO event was advertised twice, and the other two events were not advertised at all.
But the string could have also been produced by three computers:
index: 1 2 3 4 5 6 7 8 A: I . O . . I . O B: . i . . o . . . C: . . . i . . o . string: I i O i o I o O
In this interpretation, the
IO event was advertised twice, the
io event was advertised twice, and the other two events were not advertised at all. Notice that this interpretation required two computers printing
io; there could not have been just one computer printing
io twice, because it would have had to print
i twice in a row, which is not allowed.
Given a final output string, what is the maximum possible number of times that the event
IO could have been advertised?
It is guaranteed that the string has at least one valid interpretation. For example,
IOI are not valid inputs.
The first line of the input gives the number of test cases, T. T lines follow; each represents a single test case. Each case consists of a string S containing only the characters from the set
For each test case, output one line containing
Case #x: y, where
x is the test case number (starting from 1) and
y is the maximum number of times
IO could have been advertised, as described above.
icharacters plus the number of
Icharacters in S' is not less than the number of
ocharacters plus the number of
Ocharacters in S'.
is plus the number of
Is in S is equal to the number of
os plus the number of
Os in S.
5 IiOioIoO IiOOIo IoiOiO io IIIIOOOO
Case #1: 2 Case #2: 1 Case #3: 0 Case #4: 0 Case #5: 4
Sample Case #1 is the one described in the problem statement. We saw that there is an interpretation in which
IO was advertised twice. There are only two
Is and two
Os in the string, so the answer cannot be larger than this.
In Sample Case #2, notice that it is not possible that
IO was advertised twice. The only possible interpretations are as follows:
index: 1 2 3 4 5 6 A: I . . O . . B: . i O . . . C: . . . . I o string: I i O O I o
or the same but with
index: 1 2 3 4 5 6 A: I . O . . . B: . i . O . . C: . . . . I o string: I i O O I o
In either of these interpretations,
IO was advertised only once.
In Sample Case #3, there is no possible interpretation in which
IO was advertised. There must have been one computer programmed to print
Io once, and either one computer printing
iO twice, or two computers printing
iO once each.
In Sample Case #4, notice that it is possible that
O might not even show up in the string.
In Sample Case #5, an interpretation in which
IO was advertised four times requires four computers, each of which was programmed to print