There are points on a plane. Each point is described by , where . There are three types of queries needed:
X i jReflect all points in the inclusive range between points and along the -axis.Y i jReflect all points in the inclusive range between points and along the -axis.C i jCount the number of points in the inclusive range between points and in each of the quadrants. Then print a single line of four space-separated integers describing the respective numbers of points in the first, second, third, and fourth quadrants in that order.
As a reminder, the four quadrants of a graph are labeled as follows:
Given a set of points and queries, perform each query in order. For example, given points and . Initially the points are in quadrants and . The first query says to reflect points with indices from to along the -axis. After the query, and quadrants are and . The next query prints the number of points in each quadrant: 0 1 0 1. The third query says to reflect the point with index to along the -axis, so now . The points now lie in quadrants and , so the fourth query output is 0 1 1 0.
Note: Points may sometimes share the same coordinates.
Function Description
Complete the quadrants function in the editor below. It should print the results of each C type query on a new line.
quadrants has the following parameters:
- p[p[1]...p[n]]: a 2-dimensional array of integers where each element contains two integers and
- queries[queries[1]...queries[n]: an array of strings
Input Format
The first line contains a single integer, , that denotes the number of points.
Each line of the subsequent lines contains two space-separated integers that describe the respective and values for point .
The next line contains a single integer, , that denotes the number of queries.
Each of the subsequent lines contains three space-separated values that describe a query in one of the three forms defined above.
Constraints
- No point lies on the or axes.
- In all queries, .
Output Format
For each query of type C i j, print four space-separated integers that describe the number of points having indices in the inclusive range between and in the first, second, third, and fourth graph quadrants in that order.
Sample Input
4
1 1
-1 1
-1 -1
1 -1
5
C 1 4
X 2 4
C 3 4
Y 1 2
C 1 3
Sample Output
1 1 1 1
1 1 0 0
0 2 0 1
Explanation
Initially, so there is one point in each of the four quadrants. The first query results in printing 1 1 1 1.
The second query, X 2 4, reflects the points in the inclusive range between indices and along the -axis. Now .
The query C 3 4 requires that the number of points considering through be printed: 1 1 0 0
The third query, Y 1 2 requires reflection of along the -axis. Now .
The last query, C 1 3 requires that the number of points considering through be printed: 0 2 0 1