You are given two arrays aa and bb of nn positive integers each. You can apply the following operation to them any number of times:
Find the minimum possible value of max(a1,a2,…,an)⋅max(b1,b2,…,bn)max(a1,a2,…,an)⋅max(b1,b2,…,bn) you can get after applying such operation any number of times (possibly zero).
The input consists of multiple test cases. The first line contains a single integer tt (1≤t≤1001≤t≤100) — the number of test cases. Desc
The first line of each test case contains an integer nn (1≤n≤1001≤n≤100) — the length of the arrays.
The second line of each test case contains nn integers a1,a2,…,ana1,a2,…,an (1≤ai≤100001≤ai≤10000) where aiai is the ii-th element of the array aa.
The third line of each test case contains nn integers b1,b2,…,bnb1,b2,…,bn (1≤bi≤100001≤bi≤10000) where bibi is the ii-th element of the array bb.
For each test case, print a single integer, the minimum possible value of max(a1,a2,…,an)⋅max(b1,b2,…,bn)max(a1,a2,…,an)⋅max(b1,b2,…,bn) you can get after applying such operation any number of times.
3
6
1 2 6 5 1 2
3 4 3 2 2 5
3
3 3 3
3 3 3
2
1 2
2 1
18
9
2
In the first test, you can apply the operations at indices 22 and 66, then a=[1,4,6,5,1,5]a=[1,4,6,5,1,5] and b=[3,2,3,2,2,2]b=[3,2,3,2,2,2], max(1,4,6,5,1,5)⋅max(3,2,3,2,2,2)=6⋅3=18max(1,4,6,5,1,5)⋅max(3,2,3,2,2,2)=6⋅3=18.
In the second test, no matter how you apply the operations, a=[3,3,3]a=[3,3,3] and b=[3,3,3]b=[3,3,3] will always hold, so the answer is max(3,3,3)⋅max(3,3,3)=3⋅3=9max(3,3,3)⋅max(3,3,3)=3⋅3=9.
In the third test, you can apply the operation at index 11, then a=[2,2]a=[2,2], b=[1,1]b=[1,1], so the answer is max(2,2)⋅max(1,1)=2⋅1=2max(2,2)⋅max(1,1)=2⋅1=2.