Problem:
Score : 300 points

Problem Statement

There are N balls in a two-dimensional plane. The i-th ball is at coordinates (x_i, y_i).

We will collect all of these balls, by choosing two integers p and q such that p \neq 0 or q \neq 0 and then repeating the following operation:

Choose a ball remaining in the plane and collect it. Let (a, b) be the coordinates of this ball. If we collected a ball at coordinates (a - p, b - q) in the previous operation, the cost of this operation is 0. Otherwise, including when this is the first time to do this operation, the cost of this operation is 1.

Find the minimum total cost required to collect all the balls when we optimally choose p and q.

Constraints

1 \leq N \leq 50

|x_i|, |y_i| \leq 10^9

If i \neq j, x_i \neq x_j or y_i \neq y_j.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the minimum total cost required to collect all the balls.

Sample Input 1

2
1 1
2 2

Sample Output 1

1

If we choose p = 1, q = 1, we can collect all the balls at a cost of 1 by collecting them in the order (1, 1), (2, 2).

Sample Input 2

3
1 4
4 6
7 8

Sample Output 2

1

If we choose p = -3, q = -2, we can collect all the balls at a cost of 1 by collecting them in the order (7, 8), (4, 6), (1, 4).

Sample Input 3

4
1 1
1 2
2 1
2 2

Sample Output 3

2

Solution in PyPy2 (5.6.0) (judge verdict: Time Limit Exceeded)

def gcd(a, b):
    if b < 0:
        return gcd(a, -b)
    if b == 0:
        return a
    else:
        return gcd(b, a%b)

def solve():
    N = int(raw_input())
    xy = [None] * N
    for i in range(N):
        xi, yi = [int(_) for _ in raw_input().split()]
        xy[i] = (xi, yi)
    xy.sort(key = lambda x: x[0])
    pq_set = []
    def AddToPQSet(ele):
        pq, i, j = ele
        # if len(pq_set) == 0 or pq_set[0][0] > pq:
        #     pq_set.insert(0, (pq, set()))
        #     pq_set[0][1].add(i)
        #     pq_set[0][1].add(j)
        added_flag = False
        for ind in range(0, len(pq_set)):
            if pq_set[ind][0] == pq:
                subset_added = False
                for subset in pq_set[ind][1]:
                    if i in subset:
                        subset.add(j)
                        subset_added = True
                    elif j in subset:
                        subset.add(i)
                        subset_added = True
                if not subset_added:
                    tmp_set = set()
                    tmp_set.add(i)
                    tmp_set.add(j)
                    pq_set[ind][1].append(tmp_set)
                added_flag = True
            elif pq_set[ind][0] > pq:
                tmp_set = set()
                tmp_set.add(i)
                tmp_set.add(j)
                pq_set.insert(ind, (pq, [tmp_set]))
                added_flag = True
        if not added_flag:
            tmp_set = set()
            tmp_set.add(i)
            tmp_set.add(j)
            pq_set.append((pq, [tmp_set]))
        # print pq
        # print "i = " + str(i) + ", j = " + str(j)
        # print pq_set

    for i in range(N):
        for j in range(i+1, N):
            p = xy[j][0] - xy[i][0]
            q = xy[j][1] - xy[i][1]
            _gcd = gcd(p,q)
            # print "i = " + str(i) + ", j = " + str(j)
            # print p, q, _gcd
            p = p / _gcd
            q = q / _gcd
            AddToPQSet(((p,q),i,j))

    maxcntpq = 0
    # print pq_set
    for i in range(len(pq_set)):
        if len(pq_set[i][1]) > maxcntpq:
            num_subset = len(pq_set[i][1])
            cnt = 0
            for subset in pq_set[i][1]:
                cnt += len(subset)
            cnt -= num_subset
            if cnt > maxcntpq:
                maxcntpq = cnt
    print N - maxcntpq

if __name__ == '__main__':
    solve()