Picking Strings
Description
Alice has a string consisting of characters 'A', 'B' and 'C'. Bob can use the following transitions on any substring of our string in any order any number of times:
- A
BC - B
AC - C
AB - AAA
empty string
Note that a substring is one or more consecutive characters. For given queries, determine whether it is possible to obtain the target string from source.
The first line contains a string S (1 ≤ |S| ≤ 105). The second line contains a string T (1 ≤ |T| ≤ 105), each of these strings consists only of uppercase English letters 'A', 'B' and 'C'.
The third line contains the number of queries Q (1 ≤ Q ≤ 105).
The following Q lines describe queries. The i-th of these lines contains four space separated integers ai, bi, ci, di. These represent the i-th query: is it possible to create T[ci..di] from S[ai..bi] by applying the above transitions finite amount of times?
Here, U[x..y] is a substring of U that begins at index x (indexed from 1) and ends at index y. In particular, U[1..|U|] is the whole string U.
It is guaranteed that 1 ≤ a ≤ b ≤ |S| and 1 ≤ c ≤ d ≤ |T|.
Print a string of Q characters, where the i-th character is '1' if the answer to the i-th query is positive, and '0' otherwise.
Input
The first line contains a string S (1 ≤ |S| ≤ 105). The second line contains a string T (1 ≤ |T| ≤ 105), each of these strings consists only of uppercase English letters 'A', 'B' and 'C'.
The third line contains the number of queries Q (1 ≤ Q ≤ 105).
The following Q lines describe queries. The i-th of these lines contains four space separated integers ai, bi, ci, di. These represent the i-th query: is it possible to create T[ci..di] from S[ai..bi] by applying the above transitions finite amount of times?
Here, U[x..y] is a substring of U that begins at index x (indexed from 1) and ends at index y. In particular, U[1..|U|] is the whole string U.
It is guaranteed that 1 ≤ a ≤ b ≤ |S| and 1 ≤ c ≤ d ≤ |T|.
Output
Print a string of Q characters, where the i-th character is '1' if the answer to the i-th query is positive, and '0' otherwise.
Samples
AABCCBAAB
ABCB
5
1 3 1 2
2 2 2 4
7 9 1 1
3 4 2 3
4 5 1 3
10011
Note
In the first query we can achieve the result, for instance, by using transitions 
.
The third query asks for changing AAB to A — but in this case we are not able to get rid of the character 'B'.