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There is a pile of n wooden sticks. The length and weight of each stick are known in advance. The sticks are to be processed by a woodworking machine in one by one fashion. It needs some time, called setup time, for the machine to prepare processing a stick. The setup times are associated with cleaning operations and changing tools and shapes in the machine. The setup times of the woodworking machine are given as follows:
You are to find the minimum setup time to process a given pile of n wooden sticks. For example, if you have five sticks whose pairs of length and weight are (4,9) , (5,2), (2,1) , (3,5) , and (1,4) , then the minimum setup time should be 2 minutes since there is a sequence of pairs (1,4) , (3,5) , (4,9) , (2,1) , (5,2).
The input consists of T test cases. The number of test cases (T) is given in the first line of the input file. Each test case consists of two lines: The first line has an integer n , 1 ≤ n ≤ 5000 , that represents the number of wooden sticks in the test case, and the second line contains 2n positive integers l1, w1, l2, w2, ... ,ln, wn, each of magnitude at most 10000 , where li and wi are the length and weight of the i th wooden stick, respectively. The 2n integers are delimited by one or more spaces.
The output should contain the minimum setup time in minutes, one per line.
3 5 4 9 5 2 2 1 3 5 1 4 3 2 2 1 1 2 2 3 1 3 2 2 3 1
2 1 3