Once again, we have a lot of requests from coders for a challenging problem on geometry. Geometry expert Nitin is thinking about a problem with parabolas, icosahedrons, crescents and trapezoids, but for now, to encourage beginners, he chooses to work with circles and rectangles.
You are given two sequences $A_1, A_2, \ldots, A_N$ and $B_1, B_2, \ldots, B_N$. You should choose a permutation $P_1, P_2, \ldots, P_N$ of the integers $1$ through $N$ and construct $N$ rectangles with dimensions $A_1 \times B_{P_1}, A_2 \times B_{P_2}, \ldots, A_N \times B_{P_N}$. Then, for each of these rectangles, you should construct an inscribed circle, i.e. a circle with the maximum possible area that is completely contained in that rectangle.
Let $S$ be the sum of diameters of these $N$ circles. Your task is to find the maximum value of $S$.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$. 
- The third line contains $N$ space-separated integers $B_1, B_2, \ldots, B_N$. 

-----Output-----
For each test case, print a single line containing one integer ― the maximum value of $S$. It is guaranteed that this value is always an integer.

-----Constraints-----
- $1 \le T \le 50$
- $1 \le N \le 10^4$
- $1 \le A_i, B_i \le 10^9$ for each valid $i$

-----Subtasks-----
Subtask #1 (20 points):
- $A_1 = A_2 = \ldots = A_N$
- $B_1 = B_2 = \ldots = B_N$
Subtask #2 (80 points): original constraints

-----Example Input-----
2
4
8 8 10 12
15 20 3 5
3
20 20 20
10 10 10

-----Example Output-----
30
30

-----Explanation-----
Example case 1: Four rectangles with dimensions $8 \times 3$, $8 \times 5$, $10 \times 20$ and $12 \times 15$ lead to an optimal answer.

Difficulty: UNKNOWN_DIFFICULTY

Starter code:

Solutions:
for _ in range(int(input())):
	n = int(input())
	a = list(map(int, input().split()))
	b = list(map(int, input().split()))
	a.sort()
	b.sort()
	s = 0
	for i in range(n):
		s += min(a[i], b[i])
	print(s)


for t in range(int(input())):
	n = int(input())
	A = sorted(list(map(int, input().split())))
	B = sorted(list(map(int, input().split())))
	s = 0
	for i in range(n):
		s = s + min(A[i], B[i])
	print(s)


t = int(input())
while t:
	n = int(input())
	a = [int(o) for o in input().split()]
	b = [int(o) for o in input().split()]
	a.sort()
	b.sort()
	s = 0
	if a[0] == a[n - 1] and b[0] == b[n - 1]:
		print(n * min(a[0], b[0]))
	else:
		for i in range(n):
			s += min(a[i], b[i])
		print(s)
	t -= 1


t = int(input())
while t:
	n = int(input())
	a = [int(o) for o in input().split()]
	b = [int(o) for o in input().split()]
	a.sort()
	b.sort()
	if a[0] == a[n - 1] and b[0] == b[n - 1]:
		print(n * min(a[0], b[0]))
	t -= 1


import itertools
t = int(input())
for i in range(t):
	n = int(input())
	a = list(map(int, input().split()))
	a.sort()
	b = list(map(int, input().split()))
	b.sort()
	s = 0
	for (f, g) in zip(a, b):
		s += min(f, g)
	print(s)


t = int(input())
for i in range(t):
	c = 0
	n = int(input())
	a = [int(j) for j in input().split()]
	b = [int(j) for j in input().split()]
	a.sort()
	b.sort()
	for j in range(len(a)):
		if a[j] < b[j]:
			c += a[j]
		else:
			c += b[j]
	print(c)


t = int(input())
for i in range(t):
	n = int(input())
	sum = 0
	a = sorted(list(map(int, input().split())))
	b = sorted(list(map(int, input().split())))
	for j in range(n):
		if a[j] < b[j]:
			sum += a[j]
		else:
			sum += b[j]
	print(sum)


for t in range(int(input())):
	n = int(input())
	length = [int(i) for i in input().split()]
	width = [int(i) for i in input().split()]
	length.sort()
	width.sort()
	sum = 0
	for j in range(n):
		sum = sum + min(length[j], width[j])
	print(sum)


for t in range(int(input())):
	n = int(input())
	l = [int(i) for i in input().split()]
	m = [int(i) for i in input().split()]
	l.sort()
	m.sort()
	s = 0
	for j in range(n):
		s += min(l[j], m[j])
	print(s)


for _ in range(int(input())):
	n = int(input())
	a = sorted(map(int, input().split()))
	b = sorted(map(int, input().split()))
	print(sum(map(min, list(zip(a, b)))))


t = int(input())
for _ in range(t):
	n = int(input())
	a = [int(x) for x in input().split()]
	b = [int(x) for x in input().split()]
	a.sort()
	b.sort()
	ans = 0
	for i in range(n):
		ans += min(a[i], b[i])
	print(ans)


for t in range(int(input())):
	n = int(input())
	a = [int(i) for i in input().split()]
	a.sort()
	b = [int(i) for i in input().split()]
	b.sort()
	s = 0
	for i in range(n):
		s += min(a[i], b[i])
	print(s)