You are given a set of points in the 2D plane. You start at the point with the least X and greatest Y value, and end at the point with the greatest X and least Y value. The rule for movement is that you can not move to a point with a lesser X value as compared to the X value of the point you are on. Also for points having the same X value, you need to visit the point with the greatest Y value before visiting the next point with the same X value. So, if there are 2 points: (0,4 and 4,0) we would start with (0,4) - i.e. least X takes precedence over greatest Y. You need to visit every point in the plane.

-----Input-----
You will be given an integer t(1<=t<=20) representing the number of test cases. A new line follows; after which the t test cases are given. Each test case starts with a blank line followed by an integer n(2<=n<=100000), which represents the number of points to follow. This is followed by a new line. Then follow the n points, each being a pair of integers separated by a single space; followed by a new line. The X and Y coordinates of each point will be between 0 and 10000 both inclusive.

-----Output-----
For each test case, print the total distance traveled by you from start to finish; keeping in mind the rules mentioned above, correct to 2 decimal places. The result for each test case must be on a new line.

-----Example-----
Input:
3

2
0 0
0 1

3
0 0
1 1
2 2

4
0 0
1 10
1 5
2 2

Output:
1.00
2.83
18.21

For the third test case above, the following is the path you must take:
0,0 -> 1,10  
1,10 -> 1,5
1,5 -> 2,2
= 18.21

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'from math import sqrt\r\ndef distance_between_two_points(point1,point2):\r\n    a = (point1[0]-point2[0])**2 + (point1[1]-point2[1])**2\r\n    return round(sqrt(a),10)\r\n\r\nfor _ in range(int(input())):\r\n    blank = input()\r\n    N = int(input())\r\n    dic = {}\r\n    array = []\r\n    for i in range(N):\r\n        x,y = map(int, input().split())\r\n        if x not in dic.keys():\r\n            dic[x] = len(array)\r\n            array.append([x,y,y])\r\n        else :\r\n            index = dic[x]\r\n            array[index][1] = min(y,array[index][1])\r\n            array[index][2] = max(y,array[index][2])\r\n    array.sort()\r\n    ans = 0\r\n    length = len(array)\r\n\r\n    for i in range (len(array)-1):\r\n        ini = array[i]\r\n        fin = array[i+1]\r\n        ans+=(ini[2] - ini[1])\r\n        ans+=distance_between_two_points([ini[0],ini[1]],[fin[0],fin[2]])\r\n    ans += (array[-1][2] - array[-1][1])\r\n    print("{:0.2f}".format(ans))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13835