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 C (GCC 5.4.1) (judge verdict: Accepted)


#define ll				long long
#define MOD				1000000007

#include <float.h>
#include <limits.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>

FILE *in, *ans;
int tno;

int out(const char *s) {
#ifdef TEST
	char buf[8192];
	fgets(buf, sizeof(buf), ans);
	if (strcmp(buf, s)) {
		printf("err\n");
	}
#else
	printf(s);
#endif
	return 0;
}

int outi(int i) {
	char s[128];
	sprintf(s, "%d\n", i);
	out(s);
	return 0;
}

int outd(double d) {
	char s[128];
	sprintf(s, "%.10lf\n", d);
	out(s);
	return 0;
}

int outll(ll l) {
	char s[128];
	sprintf(s, "%lld\n", l);
	out(s);
	return 0;
}

int geti() {
	int i;
	fscanf(in, "%d", &i);
	return i;
}

ll getll() {
	ll l;
	fscanf(in, "%lld", &l);
	return l;
}

int getstr(char *s) {
	fscanf(in, "%s", s);
	return 0;
}

int getmin(int val1, int val2) {
	if (val1 < val2) {
		return val1;
	}
	else {
		return val2;
	}
}

int getmax(int val1, int val2) {
	if (val1 > val2) {
		return val1;
	}
	else {
		return val2;
	}
}

typedef struct data {
	int x, y;
} data;


int sortfnc(const void *v1, const void *v2) {
	data *d1 = (data *)v1;
	data *d2 = (data *)v2;

	if (d1->x > d2->x) {
		return 1;
	}
	else if (d1->x < d2->x) {
		return -1;
	}

	if (d1->y > d2->y) {
		return 1;
	}
	else if (d1->y < d2->y) {
		return -1;
	}

	return 0;
}

int n;
data datas[50];
data ptn[2500];
int pcnt;

int fnc2() {
	int i, j;

	n = geti();
	if (n <= 2) {
		return 1;
	}

	for (i = 0; i < n; i++) {
		datas[i].x = geti();
		datas[i].y = geti();
	}
	qsort(datas, n, sizeof(data), sortfnc);

	pcnt = 0;
	for (i = 0; i < n; i++) {
		for (j = i + 1; j < n; j++) {
			ptn[pcnt].x = datas[j].x - datas[i].x;
			ptn[pcnt].y = datas[j].y - datas[i].y;
			pcnt++;
		}
	}
	qsort(ptn, pcnt, sizeof(data), sortfnc);

	int x = ptn[0].x;
	int y = ptn[0].y;
	int len = 1;
	int max = len;
	for (i = 1; i < pcnt; i++) {
		if (x == ptn[i].x && y == ptn[i].y) {
			len++;
			max = getmax(max, len);
		}
		else {
			x = ptn[i].x;
			y = ptn[i].y;
			len = 1;
		}
	}

	return n - max;
}

int fnc1() {
	int ret = fnc2();
	outi(ret);
	return 0;
}

int main() {

#ifdef TEST
	for (tno = TEST_SNO; tno <= TEST_ENO; tno++) {
		char str[128];
		sprintf(str, "test%d.txt", tno);
		in = fopen(str, "r");
		sprintf(str, "ans%d.txt", tno);
		ans = fopen(str, "r");
		fnc1();
		fclose(in);
		fclose(ans);
	}
	printf("end\n");
#else
	in = stdin;
	fnc1();
#endif

	return 0;
}