Coverage

Time Limit: Java: 1000 ms / Others: 1000 ms

Memory Limit: Java: 32768 KB / Others: 32768 KB

Description

Given n points (xi, yi) (i = 1, 2 ... n) in a plane, where all xi will be distinct. After connecting the n points with staight lines in order from the leftmost point to the rightmost point, the area below the lines is called coverage. Now, it's your job to calculate the maximum coverage area, if yi (i = 1, 2 ... n) can be swapped arbitrarily.

Input

The first line of the input is an integer t (t <= 100), indicate the number of cases.

Each case starts with one integer n (2 <= n <= 1000) in a line. Then follows n lines, each consists of two integers x y (1 <= x, y <= 105) representing a point.

Cases are separated by one blank line.

Output

For each case, output the answer in a line, keep 1 digit after the decimal point.

Sample Input

2
3
1 1
2 2
3 3

3
1 2
4 1
2 5

Sample Output

4.5
10.0

Hint

None

Source

ZOJ Monthly, May 2009

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