# Large foot = High IQ?

**Computer Science**Level 5

The following \(1000\) line text file contains the data of the \(1000\) test subjects.

Find the length \(N\) of the largest subset of people in a sequence such that their foot sizes are **strictly increasing** and IQ is **strictly decreasing**.

**Details and assumptions**

Each line in the text file contains a string \((a,b)\) where \(a\) is the length of the subject's foot and \(b\) is his\her IQ.

Two people may have the same foot size, the same IQ, or even the same foot size and IQ.

All the measurements between \(1\) and \(10^4\) assume this is because weird units were used.

**Sample Input**

If the following (foot size, IQ data) for four people was given

1. (108,169)

2. (188,249)

3. (284,140)

4. (104,275)

The largest possible subset of people into a sequence whose foot size's are increasing but IQs are decreasing would be \((104,275)\rightarrow (188,249)\rightarrow(284,140)\) . And thus the length of the sequence \(N\) would be \(3\).

*Inspired from UVA problem*