Description

As the graph you see below, we named the red part "RedField".

The read part is the intersection of an ellipse and a triangle.Now, 8600's not good at math, so he wants you to help him calculate the area of the "RedField".

Input

The first line of input contains n, the number of test cases. n lines follow.Each test case contains four numbers a, b, x, y(0 < b <= a <= x),and a is the length of OA, b is the length of OB,and x, y representing the coordinate of the point P.

Output

For each test case, output the area of the "RedField",accurate up to 2 decimal places.

Sample

Input

1
1.00 1.00 2.00 2.00

Output

0.39