bronze_Logical_Moos (USACO US_Open_Contest)
Time limit: 2 seconds | Memory limit: 256 MB | Task type: batch
Algorithms: implementation, prefix sum

Farmer John has a boolean statement that is $N$ keywords long
($1 \leq N < 2 \cdot 10^5$, $N$ odd). Only $\texttt{true}$ or $\texttt{false}$
appear in odd positions, while only $\texttt{and}$ and $\texttt{or}$ appear in
even positions.
A phrase of the form $x\text{ OPERATOR }y$, where $x$ and $y$ are either
$\texttt{true}$ or $\texttt{false}$, and $\text{OPERATOR}$ is $\texttt{and}$ or
$\texttt{or}$, evaluates as follows:
$x\texttt{ and }y$: This evaluates to true if both $x$ and $y$ are true, and
false otherwise.
$x\texttt{ or }y$: This evaluates to true if either $x$ or $y$ is true, and
false otherwise.
When evaluating the statement, FJ has to take the order of precedence in Moo
Language into account. Similar to C++, $\texttt{and}$ takes priority over
$\texttt{or}$. More specifically, to evaluate the statement, repeat the
following step until the statement consists of only one keyword.
If the statement contains an $\texttt{and}$, choose any of them and replace
the phrase surrounding it with its evaluation.
Otherwise, the statement contains an $\texttt{or}$. Choose any of them and
replace the phrase surrounding it with its evaluation.
It may be proven that if multiple phrases can be evaluated during a given step,
it does not matter which one is chosen; the statement will always evaluate to
the same value.
FJ has $Q$ $(1 \leq Q \leq 2 \cdot 10^5)$ queries. In each query, he gives you
two integers $l$ and $r$ ($1 \leq l \leq r \leq N$, $l$ and $r$ are both odd),
and deletes the segment from keyword $l$ to keyword $r$ inclusive. In turn, he
wishes to replace the segment he just deleted with just one simple
$\texttt{true}$ or $\texttt{false}$ so that the whole statement evaluates to a
certain boolean value. Help FJ determine if it's possible!
INPUT FORMAT (input arrives from the terminal / stdin):
The first line contains $N$ and $Q$.
The next line contains $N$ strings, a valid boolean statement.
The following $Q$ lines contain two integers $l$ and $r$, and a string
$\texttt{true}$ or $\texttt{false}$, denoting whether he wants the whole
statement to evaluate to true or false.
OUTPUT FORMAT (print output to the terminal / stdout):
Output a string of length $Q$, where the $i$'th character is Y if the $i$'th
query is possible, otherwise N.
SAMPLE INPUT:
5 7
false and true or true
1 1 false
1 3 true
1 5 false
3 3 true
3 3 false
5 5 false
5 5 true
SAMPLE OUTPUT:
NYYYNYY
Let's analyze the first query:
If we were to replace delete the segment $[1, 1]$ and replace it with
$\texttt{true}$, then the whole statement becomes:
true and true or true
We evaluate the $\texttt{and}$ keyword from at position $2$ and obtain
true or true
Since we have no $\texttt{and}$ keywords left, we have to evaluate the
$\texttt{or}$ keyword. After evaluation, all that is left is
true
It can be shown that if we were to replace the segment with $\texttt{false}$,
the statement will still evaluate to $\texttt{true}$, so we output N since the
statement cannot possibly evaluate to $\texttt{false}$.
For the second query, we can replace the segment $[1, 3]$ with $\texttt{true}$
and the whole statement will evaluate to $\texttt{true}$, so we output Y.
For the third query, since $[1, 5]$ is the whole statement, we can replace it
with anything, so we output Y.
SAMPLE INPUT:
13 4
false or true and false and false and true or true and false
1 5 false
3 11 true
3 11 false
13 13 true
SAMPLE OUTPUT:
YNYY
SCORING:
Inputs 3-5: $N,Q\le 10^2$
Inputs 6-8: $N,Q\le 10^3$
Inputs 9-26: No additional constraints.
Problem credits: Chongtian Ma

Starter code:

Grader code:

Setup script:

Evaluation script: