B. Gaz Map
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Gaz is an infinite city. The streets of this city are as follows :

Gaz Map

The streets of this city can be introduced on the two-dimensional coordinate system as follows :

  • A horizontal street coinciding with the $$$x-$$$axis.
  • A vertical street coinciding with the $$$y-$$$axis.
  • For every natural number $$$n$$$, there is a circular street with radius $$$n$$$ with the center of $$$(0, 0)$$$ coordinate.

We know that Alice is currently at a junction with coordinate $$$(x_1, y_1)$$$ and Bob is currently at a junction with coordinate $$$(x_2, y_2)$$$. A junction is a point at intersection of two streets. For example, $$$(0,1)$$$ and $$$(0,-1)$$$ are junctions formed from intersection of horizontal street and circular streets with radius $$$1$$$.

Alice wants to know the shortest distance that she has to walk in the streets of Gaz to reach Bob.

Input

In the first line of input you'll be given a number $$$t$$$ $$$-$$$ the number of the testcases.

$$$$$$1 \le t \le 100$$$$$$

In each of the next $$$t$$$ lines, you'll receive $$$4$$$ integers $$$x_1, y_1, x_2, y_2$$$ which show the coordinates of the junctions where Alice and Bob are located.

$$$$$$-10^9 \le x_1, y_1, x_2, y_2 \le 10^9$$$$$$

It is guaranteed that at least one of $$$x_1, y_1$$$ and at least one of $$$x_2, y_2$$$ will be $$$0$$$.

Output

For each test, print only one line containing a single floating-point number $$$-$$$ the minimum answer. Your answer will be considered correct if its absolute or relative error does not exceed $$$10^{-6}$$$.

Example
Input
4
2 0 -4 0
0 3 5 0
0 -7 0 0
0 -5 0 -5
Output
6.000000
6.712389
7.000000
0.000000
Note

Explanation of testcase $$$1$$$ :

The shortest path between these two junctions is a path in the form of a straight line.

$$$$$$\sqrt {(2 - (-4))^2 + (0 - 0)^2} = 6$$$$$$

Explanation of testcase $$$2$$$ :

The shortest path is like this :

$$$$$$\frac{1}{4} \times (2\pi \times 3) + \sqrt{(5 - 3)^2 + (0 - 0)^2} = \frac{3\pi}{2} + 2 \simeq 6.712389$$$$$$