Wooden Sticks

Time Limit: 2 Seconds
Memory Limit: 65536 KB

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 (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).

**Input **

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 n 2 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.

**Output **

The output should contain the minimum setup time in minutes, one per line.

**Sample Input **

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

Output for the Sample Input

2

1

3

Source:

**Asia 2001, Taejon (South Korea)**
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