You are given two arrays, A and B, of equal size N. The task is to find the minimum value of A[0] * B[0] + A[1] * B[1] +…+ A[N-1] * B[N-1], where shuffling of elements of arrays A and B is allowed.

Input:
The first line of input contains an integer T denoting the no of test cases. Then T test cases follow. Each test case contains three lines. The first line contains an integer N denoting the size of the arrays. In the second line are N space separated values of the array A[], and in the last line are N space separated values of the array B[].

Output:
For each test case, print the minimum sum.

Constraints:
1 <= T <= 100
1 <= N <= 10⁷
1 <= A[] <= 10¹⁸

Example:
Input:
2
3 
3 1 1
6 5 4
5
6 1 9 5 4
3 4 8 2 4
Output:
23 
80

Explanation:
For testcase1: 1*6+1*5+3*4 = 6+5+12 = 23 is the minimum sum
For testcase2: 2*9+3*6+4*5+4*4+8*1 =18+18+20+16+8 = 80 is the minimum sum