You are given set of n points in 5-dimensional space. The points are labeled from 1 to n. No two points coincide.

We will call point a bad if there are different points b and c, not equal to a, from the given set such that angle between vectors <image> and <image> is acute (i.e. strictly less than <image>). Otherwise, the point is called good.

The angle between vectors <image> and <image> in 5-dimensional space is defined as <image>, where <image> is the scalar product and <image> is length of <image>.

Given the list of points, print the indices of the good points in ascending order.

Input

The first line of input contains a single integer n (1 ≤ n ≤ 103) — the number of points.

The next n lines of input contain five integers ai, bi, ci, di, ei (|ai|, |bi|, |ci|, |di|, |ei| ≤ 103) — the coordinates of the i-th point. All points are distinct.

Output

First, print a single integer k — the number of good points.

Then, print k integers, each on their own line — the indices of the good points in ascending order.

Examples

Input

6
0 0 0 0 0
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1


Output

1
1


Input

3
0 0 1 2 0
0 0 9 2 0
0 0 5 9 0


Output

0

Note

In the first sample, the first point forms exactly a <image> angle with all other pairs of points, so it is good.

In the second sample, along the cd plane, we can see the points look as follows:

<image>

We can see that all angles here are acute, so no points are good.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Allen Li
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        FiveD solver = new FiveD();
        solver.solve(1, in, out);
        out.close();
    }

    static class FiveD {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            Point[] points = new Point[n];

            for (int i = 0; i < n; i++) {
                points[i] = new Point(in.nextInt(), in.nextInt(), in.nextInt(), in.nextInt(), in.nextInt());
            }
            boolean[] bad = new boolean[n];
            outer:
            for (int i = 0; i < n; i++) {

                for (int j = 0; j < n; j++) {
                    if (i == j)
                        continue;
                    for (int k = 0; k < n; k++) {
                        if (j == k)
                            continue;
                        Point v1 = points[j].subtract(points[i]);
                        Point v2 = points[k].subtract(points[i]);
                        double ang = Math.toDegrees(Math.acos((v1.dot(v2)) / (v1.mag() * v2.mag())));
                        if (ang < 90) {
                            bad[i] = true;
                            continue outer;
                        }
                    }
                }
            }
            int res = 0;
            for (int i = 0; i < n; i++) {
                if (!bad[i])
                    res++;
            }
            out.println(res);
            for (int i = 0; i < n; i++) {
                if (!bad[i]) {
                    out.println(i + 1);
                }
            }
        }

        class Point {
            int a;
            int b;
            int c;
            int d;
            int e;

            Point subtract(Point p) {
                return new Point(a - p.a, b - p.b, c - p.c, d - p.d, e - p.e);
            }

            public Point(int a, int b, int c, int d, int e) {
                this.a = a;
                this.b = b;
                this.c = c;
                this.d = d;
                this.e = e;
            }

            int dot(Point p) {
                return a * p.a + b * p.b + c * p.c + d * p.d + e * p.e;
            }

            double mag() {
                return Math.sqrt(a * a + b * b + c * c + d * d + e * e);
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

