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:
(a) The setup time for the first wooden stick is 1 minute.
(b) Right after processing a stick of length l and weight w , the machine will
need no setup time for a stick of length l' and weight w' if l ≤ l' and w ≤ w'.
Otherwise, it will need 1 minute for setup.
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
( 9 , 4 ) , ( 2 , 5 ) , ( 1 , 2 ) , ( 5 , 3 ) , and ( 4 , 1 ) , then the minimum
setup time should be 2 minutes since there is a sequence of pairs ( 4 , 1 ) ,
( 5 , 3 ) , ( 9 , 4 ) , ( 1 , 2 ) , ( 2 , 5 ) .
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.
4 9 5 2 2 1 3 5 1 4
2 2 1 1 2 2
1 3 2 2 3 1
The output should contain the minimum setup time in minutes, one per line.