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Description:

Input:

The first line contains a positive integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. In the following lines are written $$$t$$$ test cases.

The description of each test case is one line, which contains four integers $$$a$$$, $$$b$$$, $$$c$$$ and $$$r$$$ ($$$-10^8 \le a,b,c \le 10^8$$$, $$$0 \le r \le 10^8$$$) — the coordinates of the starting and ending points of the path, the base station, and its coverage radius, respectively.

Any of the numbers $$$a$$$, $$$b$$$ and $$$c$$$ can be equal (either any pair or all three numbers). The base station can be located both on the route of Polycarp and outside it.

Output:

Print $$$t$$$ numbers — answers to given test cases in the order they are written in the test. Each answer is an integer — the number of minutes during which Polycarp will be unavailable during his movement.

Sample Input:

9
1 10 7 1
3 3 3 0
8 2 10 4
8 2 10 100
-10 20 -17 2
-3 2 2 0
-3 1 2 0
2 3 2 3
-1 3 -2 2

Sample Output:

7
0
4
0
30
5
4
0
3

Note:

The following picture illustrates the first test case.

Polycarp goes from $$$1$$$ to $$$10$$$. The yellow area shows the coverage area of the station with a radius of coverage of $$$1$$$, which is located at the point of $$$7$$$. The green area shows a part of the path when Polycarp is out of coverage area.