B. Easy Geometry
time limit per test
2 с
memory limit per test
256 megabytes
input
standard input
output
standard output

Boboge is currently at $$$(x_1, y_1)(y_1 \gt 0)$$$, there is a river at $$$y=0$$$, and his destination is at $$$(x_2, y_2)(y_2 \gt 0)$$$. He needs to get some water from the river first, then go to the destination. What's the minimum distance he has to travel?

A example.
Input

The first line contains an integer $$$T(1 \le T \le 10^5)$$$ — the number of test cases. The description of the test cases follows.

The only line of each test case consists of $$$4$$$ integers: $$$x_1,y_1,x_2,y_2(-10^9 \le x_1, x_2 \le 10 ^ 9, 0 \lt y_1, y_2 \le 10^9)$$$ — the positions.

Output

For each test case, print the minimum distance.

Your answer is considered correct if its absolute or relative error does not exceed $$$10^{-6}$$$.

Formally, let your answer be $$$x$$$, and the jury's answer be $$$y$$$. Your answer is accepted if and only if $$$\frac{|x-y|}{max(1,|y|)} \le 10^{-6}$$$.

Examples
Input
2
0 1 2 1
-10 10 -20 20
Output
2.8284271247
31.6227766017
Input
1
-1000000000 1000000000 1000000000 1000000000
Output
2828427124.7461900711