There are many students in the University of Hong Kong. Some of them are hardworking, some are clever and some are both hardworking and clever. We use two real numbers to describe a student. HWP (Hard Working Point) describes how hardworking she is, and CP (Clever Point) describes how clever she is.

There are many courses in the University of Hong Kong. For some of the courses, like physics, a student must work very hard and do a lot of exercise to pass the course. So students with high HWP can pass it easily. Of course, if a student is clever, it also helps a little. For some other courses, like artificial intelligence, CP helps a lot and HWP helps a little. So we can also use two real numbers ~x~ and ~y~ to describe a course. A student can pass the course if and only if

$$\displaystyle \textbf{HWP} \times x + \textbf{CP} \times y > 1$$

There is a course management system, teachers can create new courses or cancel courses, and students can know if they can pass all the courses that exist right now.

Input Specification

The first line of the input contains one integer ~M~, representing the number of operations.

Each of the following ~M~ lines contains some numbers describing an operation.

• If the first number is ~0~, it means a teacher creates a new course. Then the following three numbers in this line are ~x,y,id~ of the course. ~(0.001 < x,y < 1000, 0 \le id \le 100\,000)~, and ~id~ is an integer)
• If the first number is ~1~, it means a teacher cancels an old course. Then the following one number in this line represents the ~id~ of the course to cancel. It is guaranteed that this course exists before deleting.
• If the first number is ~2~, it means a student wants to know if she can pass all the courses that exist right now, the following two numbers in this line are ~\textbf{HWP}~ and ~\textbf{CP}~ of the student. ~(0.001 < \textbf{HWP},\textbf{CP} < 1000)~

To avoid precision problems, for any student and any course, ~|\textbf{HWP} \times x + \textbf{CP} \times y - 1| > 10^{-8}~.

• For ~20\%~ of the test cases, ~M \le 1000~.
• For other ~40\%~ of the test cases, there is no cancel operation.
• For ~100\%~ of the test cases, ~M \le 100\,000~.

Output Specification

For each student, if she can pass all the courses, print a line with single integer ~1~. Otherwise, print a line with single integer ~0~.

Sample Input 1

8
0 1 2 1
0 5 0.2 2
2 0.1 2
2 0.1 3
0 0.13 0.59 3
0 2.44 0.78 4
2 3 1
2 1 3

Sample Output 1

0
1
0
1

Sample Input 2

10
0 1 2 1
0 5 0.2 2
2 0.1 2
2 0.1 3
1 2
2 0.1 2
0 0.13 0.59 3
0 2.44 0.78 4
2 3 1
2 1 3

Sample Output 2

0
1
1
0
1