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Max Separation
Time Limit: 1000MSMemory Limit: 10000K
Total Submissions: 78Accepted: 27

Description

Max separation problem is an interesting geometry problem: given N+1 point sets S0,S1,...,SN in 2-dimension panel, which including k0,k1,...kN points. These points can represented by Cartesian-coordinate as follows: Si={(xi1,yi1),...,(xik,yik)},i=0,1,...,N.

If these is a line separating S0 and p(p<=N) point sets in S1,S2,...,SN, that means S0 is in one side of the line, and the p sets of S1,S2...SN are in the other side of the line, we called S0 is p-separated with respect to S1,S2,...SN.

Now give you the point sets S0,S1,...SN, find the max value of p.

Input

The first line of the input file contains an integer N(1 <= N<=30). The next N+1 line contains the point set S0,S1,...SN, that is, in the next i'th line, there are all the points coordinate in Si-1. One point is represented by x and y coordinate, separated by a comma. And every point is preceded a semicolon. Every line of Si configuration is ended by '#'. All coordinates are integers. See the sample input for detailed information.

Output

Output contains only one line -- the max separation p.

Sample Input

2
0,0;1,1;#
1,0;0,1;#
1,0;0,-1;#

Sample Output

1

Source

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