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If you notice incorrect translations in Contester, please let author know.

Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
: , .

N points are on a plane. You have to find the minimal number of straight lines, so that each point would belong to at least one line. Besides, if you have to use more than one line, then all the lines should be parallel to each other.

Input
In the first line of input file an integer number N is written - number of points on a plane (1 ≤ N ≤ 250). In the next N lines points coordinates are written. All coordinates are integer numbers with absolute value not greater that 106.
Output
Write a single number - the answer to this problem.

Input 1 Output 1 Input 2 Output 2 Input 3 Output 3
3
0 0
2 0
10 0
1
4
0 0
1 0
0 1
1 1
2
4
0 0
1 0
2 1
2 3
3

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