Posted here is the code I've written for wormhole in one. It worked on 
every test I ran on it, and it follows the logic of the analysis, and it 
still doesnt work.
Can anyone spot the mistake? I would love to know what it was, so I could 
fix it the next time, because I can't seem to find any mistake.
(the code is a bit dirty because i've tried some fixes, but it should still 
work)

def main():
    N = int(input())
    holes = []
    for i in range(N):
        a = [int(x) for x in input().split()]
        holes.append(tuple(a))
    if N <= 4:
        return N
    slants = {}
    actual_lines = {}
    for cur_hole in holes:
        for j in holes:
            if j == cur_hole:
                continue
            if cur_hole[0] == j[0]:
                slant = 'inf'
            else:
                slant = float(cur_hole[1] - j[1]) / float(cur_hole[0] - 
j[0])
            slants.setdefault(slant, [set(), 2])
            slants[slant][0].add(cur_hole)
            slants[slant][0].add(j)
            if slant == 'inf':
                y = cur_hole[0]
            else:
                y = cur_hole[1] - slant * cur_hole[0]
            yy = (slant, y)
            #actual_lines.setdefault(yy, set([]))
            #actual_lines[yy].add(cur_hole)
            #actual_lines[yy].add(j)
    #for i in actual_lines:
    #    if len(actual_lines[i]) % 2:
    #        slants[i[0]][1] ^= 3
    a = slants[max(slants, key=lambda x: len(slants[x][0]) + 
(len(slants[x][0])%2==0))]
    a = len(a[0]) + (len(a[0])%2==0)
    return min(N, max(a+1,4))


num_of_cases = [int(x) for x in input().split()][0]
for p in range(num_of_cases):
    output = main()
    print("Case #{0}: {1}".format(p + 1, output))

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