A river runs through a town in a perfectly straight line. On the map the river is given by two different points and that it passes through, and it continues forever in both directions.
The town wants to know how its houses are split between the two banks. A house is on the left bank if it lies to the left of somebody standing at and looking towards , and on the right bank if it lies to their right. Some houses were built right on top of the river and belong to neither bank.
Your task is to count the houses on each bank.
Input
The first line contains a single integer - the number of testcases.
- The first line of each testcase contains a single integer - the number of houses.
- The second line contains four integers , , , - the two points that define the river. The points are different.
- Each of the next lines contains two integers and - the position of one house.
Output
For every testcase print a single line with three integers: the number of houses on the left bank, the number on the right bank, and the number standing on the river.
Example
2 5 0 0 4 4 0 4 1 4 4 0 2 2 5 1 3 0 0 1000000000 1000000000 1000000000 -1000000000 -1000000000 1000000000 5 5
2 2 1 1 1 1
In the first testcase the river goes diagonally through the origin. The houses at and are above it, the houses at and are below it, and the house at is standing in the water.
Constraints