Farmer John has a boolean statement that is N keywords long (1≤N<2⋅105, N odd). Only true or false appear in odd positions, while only and and or appear in even positions.
A phrase of the form x OPERATOR y, where x and y are either true or false, and OPERATOR is and or or, evaluates as follows:
x and y: This evaluates to true if both x and y are true, and false otherwise.
x 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++, and takes priority over or. More specifically, to evaluate the statement, repeat the following step until the statement consists of only one keyword.
1.If the statement contains an and, choose any of them and replace the phrase surrounding it with its evaluation.
2.Otherwise, the statement contains an 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≤Q≤2⋅105 ) queries. In each query, he gives you two integers l and r (1≤l≤r≤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 true or 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 true or 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 true, then the whole statement becomes:
true and true or true
We evaluate the and keyword from at position 2 and obtain
true or true
Since we have no and keywords left, we have to evaluate the or keyword. After evaluation, all that is left is
true
It can be shown that if we were to replace the segment with false, the statement will still evaluate to true, so we output N since the statement cannot possibly evaluate to false.
For the second query, we can replace the segment [1,3] with true and the whole statement will evaluate to 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≤102
Inputs 6-8: N,Q≤103
Inputs 9-26: No additional constraints.
Problem credits: Chongtian Ma
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