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.*;
import java.util.StringTokenizer;

/**
 * Created by fly on 9/4/17.
 */
public class Main {
    public static int mod = 1000000007;

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.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[] candid = new boolean[n];
        for (int i = 0; i < n; ++i) {
            again:
            if (!candid[i]) {
            for (int j = 0; j < n; ++j) {
                for (int k = 0; k < n; ++k) {
                    if (i != j && i != k && j != k) {
                            if (good(new Vec(points[i], points[j]), new Vec(points[i], points[k]))) {
                                candid[j] = candid[k] = true;
                            } else {
                                candid[i] = true;
                                break again;
                            }
                        }
                    }
                }
            }
        }
        int count = 0;
        for(int i = 0; i < n; ++i) {
            if(!candid[i]) ++count;
        }
        System.out.println(count);
        if(count >0) {
            for (int i = 0; i < n; ++i) {
                if (!candid[i])
                    System.out.println(i + 1);
            }
        }
        out.close();
    }

    static boolean good(Vec i, Vec j) {
        return i.x * j.x + i.y * j.y + i.z * j.z + i.w * j.w + i.v * j.v <= 0;
    }

    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) {
                    e.printStackTrace();
                }
            }
            return tokenizer.nextToken();
        }

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

        public long nextLong() {
            return Long.parseLong(next());
        }
    }

    static class Point {
        int x, y, z, w, v;

        public Point(int x, int y, int z, int w, int v) {
            this.x = x;
            this.y = y;
            this.z = z;
            this.w = w;
            this.v = v;
        }
    }

    static class Vec {
        int x, y, z, w, v;

        public Vec(Point from, Point to) {
            this.x = to.x - from.x;
            this.y = to.y - from.y;
            this.z = to.z - from.z;
            this.w = to.w - from.w;
            this.v = to.v - from.v;
        }
    }
}
