# Chop Chop

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Limits 1.5s, 256 MB

There is a convex polygon $A%$ of $n$ vertices and you want to divide it into two convex polygons $P$ and $Q$ such that their areas are equal (half of $A$) and the sum of perimeters of $P$ and $Q$ is minimum possible.

## Input

The first line of the input is an integer $T$ which denotes the number of test cases.

For each test case, the first line contains an integer $n$, denoting the number of vertices in the polygon $A$. $n$ lines follow, $i^{th}$ line containing two real numbers (with four digit precision after decimal point) $x_i, ~y_i$ denoting the co-ordinate of the $i^{th}$ vertex of $A$ in a counter-clockwise manner.

Constraints:

• $1 \le T \le 100$.

• $3 \le n \le 2 \times 10^5$.

• $-10^7 \le x_i, ~y_i \le 10^7$.

• Sum of $n$ across all testcases is less than or equal to $2 \times 10^5$.

## Output

For each test case, output the minimum total sum of perimeters of $P$ and $Q$ on a single line.

Your output will be considered correct if the absolute or relative error is less than or equal to $10^{-6}$.

## Sample

InputOutput
1
3
0.0000 0.0000
1000.0000 0.0000
500.0000 1.0000

2002.0019989980