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.

Examples

Input

2
1 1
2 2


Output

1


Input

3
1 4
4 6
7 8


Output

1


Input

4
1 1
1 2
2 1
2 2


Output

2
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.NavigableSet;
import java.util.Objects;
import java.util.Set;
import java.util.TreeSet;

public class Main {
    private static class Pos {
        final int x;
        final int y;
        Pos(int x, int y) {
            this.x = x;
            this.y = y;
        }
        @Override
        public int hashCode() {
            return Objects.hash(x, y);
        }
        @Override
        public boolean equals(Object obj) {
            if (this == obj)
                return true;
            if (obj == null)
                return false;
            if (!(obj instanceof Pos))
                return false;
            Pos other = (Pos)obj;
            return x == other.x && y == other.y;
        }
    }
    static void solve(MyScanner in, PrintWriter out) {
        int n = in.nextInt();
        if (n == 1) {
            out.println(1);
            return;
        }
        Pos[] posArray = new Pos[n];
        for (int i = 0; i < n; i++) {
            int x = in.nextInt();
            int y = in.nextInt();
            posArray[i] = new Pos(x, y);
        }
        Arrays.sort(posArray, (a, b) -> {
            if (a.x < b.x)
                return -1;
            if (a.x > b.x)
                return 1;
            if (a.y < b.y)
                return -1;
            if (a.y > b.y)
                return 1;
            return 0;
        });
        Map<Pos, Integer> m = new HashMap<>();
        for (int i = 0; i < n; i++) {
            Pos a = posArray[i];
            Set<Pos> s = new HashSet<>();
            for (int j = i + 1; j < n; j++) {
                Pos b = posArray[j];
                Pos pos = new Pos(b.x - a.x, b.y - a.y);
                if (s.contains(pos))
                    continue;
                s.add(pos);
                Integer c = m.get(pos);
                if (c == null)
                    m.put(pos, 1);
                else
                    m.put(pos, c + 1);
            }
            s.clear();
        }
        NavigableSet<Integer> ns = new TreeSet<>(m.values());
        Integer max = ns.last();
        out.println(n - max);
    }

    public static void main(String[] args) {
        PrintWriter w = new PrintWriter(System.out);
        solve(new MyScanner(System.in), w);
        w.flush();
    }

    static final class MyScanner {
        static final int BUFFER_SIZE = 8192;
        private final InputStream in;
        private final byte[] buffer = new byte[BUFFER_SIZE];
        private int point;
        private int readLength;
        MyScanner(InputStream in) {
            this.in = in;
        }
        private int readByte() {
            if (point < readLength) {
                int result = buffer[point];
                point += 1;
                return result;
            }
            try {
                readLength = in.read(buffer);
            } catch (IOException e) {
                throw new AssertionError(null, e);
            }
            if (readLength == -1) {
                return -1;
            }
            point = 1;
            return buffer[0];
        }
        private static boolean isPrintableCharExceptSpace(int c) {
            return 33 <= c && c <= 126;
        }
        String next() {
            int c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            assert c != -1;
            StringBuilder b = new StringBuilder();
            do {
                b.appendCodePoint(c);
                c = readByte();
            } while (c != -1 && isPrintableCharExceptSpace(c));
            return b.toString();
        }
        long nextLong() {
            int c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            assert c != -1;
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = readByte();
            }
            long result = 0L;
            do {
                assert '0' <= c && c <= '9' : c;
                result = result * 10L + (c - '0');
                c = readByte();
            } while (c != -1 && isPrintableCharExceptSpace(c));
            return minus ? -result : result;
        }
        int nextInt() {
            long n = nextLong();
            assert Integer.MIN_VALUE <= n && n <= Integer.MAX_VALUE : n;
            return (int)n;
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        int[] nextIntArray(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextInt();
            }
            return result;
        }
        private static boolean allSameLength(int[] a, int[] b, int[]... c) {
            if (a.length != b.length) {
                return false;
            }
            for (int i = 0; i < c.length; i++) {
                if (a.length != c[i].length) {
                    return false;
                }
            }
            return true;
        }
        private static boolean allSameLength(char[] a, char[] b, char[]... c) {
            if (a.length != b.length) {
                return false;
            }
            for (int i = 0; i < c.length; i++) {
                if (a.length != c[i].length) {
                    return false;
                }
            }
            return true;
        }
        void nextVerticalIntArrays(int[] a, int[] b, int[]... c) {
            assert allSameLength(a, b, c);
            for (int i = 0; i < a.length; i++) {
                a[i] = nextInt();
                b[i] = nextInt();
                for (int[] d : c) {
                    d[i] = nextInt();
                }
            }
        }
        long[] nextLongArray(int n) {
            long[] result = new long[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextLong();
            }
            return result;
        }
        char nextChar() {
            int c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            assert c != -1;
            return (char)c;
        }
        char[] nextCharArray(int n) {
            char[] result = new char[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextChar();
            }
            return result;
        }
        char[][] next2dCharArray(int n, int m) {
            char[][] result = new char[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    result[i][j] = nextChar();
                }
            }
            return result;
        }
        void nextVerticalCharArrays(char[] a, char[] b, char[]... c) {
            assert allSameLength(a, b, c);
            for (int i = 0; i < a.length; i++) {
                a[i] = nextChar();
                b[i] = nextChar();
                for (char[] d : c) {
                    d[i] = nextChar();
                }
            }
        }
    }
}
