Parity game
Now and then you play the following game with your friend. Your friend
writes down a sequence consisting of zeroes and ones. You choose a
continuous subsequence (for example the subsequence from the third to
the fifth digit inclusively) and ask him, whether this subsequence
contains even or odd number of ones. Your friend answers your question
and you can ask him about another subsequence and so on. Your task is
to guess the entire sequence of numbers.
You suspect some of your friend's answers may not be correct and you
want to convict him of falsehood. Thus you have decided to write a
program to help you in this matter. The program will receive a series
of your questions together with the answers you have received from
your friend. The aim of this program is to find the first answer which
is provably wrong, i.e. that there exists a sequence satisfying
answers to all the previous questions, but no such sequence satisfies
this answer.
Input:
The first line of input file PARITY.IN contains one number, which is
the length of the sequence of zeroes and ones. This length is less or
equal to 1000000000. In the second line, there is one positive integer
which is the number of questions asked and answers to them. The number
of questions and answers is less or equal to 5000. The remaining lines
specify questions and answers. Each line contains one question and the
answer to this question: two integers (the position of the first and
last digit in the chosen subsequence) and one word which is either
`even' or `odd' (the answer, i.e. the parity of the number of ones in
the chosen subsequence, where `even' means an even number of ones and
`odd' means an odd number).
Output:
There is only one line in output file PARITY.OUT containing one
integer X. Number X says that there exists a sequence of zeroes and
ones satisfying first X parity conditions, but there exists none
satisfying X+1 conditions. If there exists a sequence of zeroes and
ones satisfying all the given conditions, then number X should be the
number of all the questions asked.
Example 1:
PARITY.IN
10
5
1 2 even
3 4 odd
5 6 even
1 6 even
7 10 odd
PARITY.OUT
3
Example 2:
PARITY.IN
10
5
1 2 even
1 4 even
2 4 odd
1 10 even
3 10 even
PARITY.OUT
5