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문제

The Manhattan in the New York City has really a nice topology. So nice, it is often idealized to a rectangular grid. If you want to go from corner A = (Ax, Ay) to corner B = (Bx, By), the shortest way has length |Ax − Bx| + |Ay − By|. Or so they told you in school.

The truth is, the correct definition of a Manhattan metric has to involve the Broadway – a road that leads across the neatly aligned system of streets and avenues. In this problem we finally correct this horrible mistake made by the mathematical community.

Given the two corners A = (Ax, Ay),B = (Bx, By) and three rational numbers P, Q, R that describe the Broadway, your task is to find the length of the shortest path between points A and B.

• For each integer Z, there is an avenue described by the equation x = Z.
• For each integer Z, there is a street described by the equation y = Z.
• The Broadway is described by the equation Px + Qy = R.

When moving from A to B, we can only move along the roads and change roads at intersections.

입력

The first line of the input file contains an integer T specifying the number of test cases. Each test case is preceded by a blank line.

Each test case consists of one line containing seven numbers: four integers Ax, Ay, Bx, By specifying the points A = (Ax, Ay) and B = (Bx, By), and three rational numbers P, Q, R specifying the Broadway as explained above.

출력

For each test case output a single line containing the length of the shortest path from A to B. Output a sufficient number of decimal places. Your output will be judged as correct if it has an absolute or relative error at most 10−9.

제한

P, Q, R is given to exactly 10 decimal places.

Easy (1점)

• -1 000 ≤ Ax, Ay, Bx, By ≤ 1 000
• -200 ≤ P ≤ 200
• Q = 1
• -20 000 ≤ R ≤ 20 000

Hard (2점)

• -1 000 000 ≤ Ax, Ay, Bx, By ≤ 1 000 000
• -25 ≤ P ≤ 25
• Q = 1
• -2 000 000 ≤ R ≤ 2 000 000

예제 입력 1

2

2 0 -1 1 1.0 1.0 1.0

-2 3 4 -1 1.0 -0.1 0.47


예제 출력 1

3.414213562373
10


채점 및 기타 정보

• 예제는 채점하지 않는다.