There are \(N\) numbers from \(1\) to \(N\) and your task is to create a permutation such that the cost of the permutation is minimum. For each number, there is a left and right cost. To put number  \(p\) \((1 \leq p \leq N)\) at the \(i^{th}\) index, it costs \(L_p *(i - 1) + R_p*(N-i-1)\) where \(L[]\) and \(R[]\) cost is given.

You do not need to find that permutation but you need to find the total minimum possible cost of the permutation.

Input format

• The first line contains \(T\) denoting the number of test cases.
• The first line of each test case contains the number \(N\).
• The next line of each test case contains \(N\) integers to indicate the left cost. 
• The next line of each test case contains \(N\) integers to indicate the right cost.

Output format

For each test case, print a single line containing one integer that denotes the minimum cost of the permutation.

Constraints

\(1 \leq T \leq 20\)

\(2 \leq N \leq 10^5\)

\(1 \leq L_i,R_i \leq 10^7\) for each \(1 \leq i \leq N\)