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.HashSet;
import java.util.StringTokenizer;
import java.util.Set;
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 Yogesh Kumar a.k.a DREAMPLAY
 */
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);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
//        System.out.println(Math.toDegrees(Math.acos(0.5)));
            int n = in.nextInt();
            if (n >= 100) {
                out.print(0);
            } else {
                int[] a = new int[105];
                int[] b = new int[105];
                int[] c = new int[105];
                int[] d = new int[105];
                int[] e = new int[105];
                for (int i = 1; i <= n; i++) {
                    a[i] = in.nextInt();
                    b[i] = in.nextInt();
                    c[i] = in.nextInt();
                    d[i] = in.nextInt();
                    e[i] = in.nextInt();
                }

                Set<Integer> bad = new HashSet<>();

                for (int i = 1; i <= n; i++) {
                    for (int j = 1; j <= n; j++) {
                        for (int k = 1; k <= n; k++) {
                            if (i == j || j == k || k == i) {
                                continue;
                            }

                            long ax = a[j] - a[i];
                            long bx = b[j] - b[i];
                            long cx = c[j] - c[i];
                            long dx = d[j] - d[i];
                            long ex = e[j] - e[i];

                            long ay = a[k] - a[i];
                            long by = b[k] - b[i];
                            long cy = c[k] - c[i];
                            long dy = d[k] - d[i];
                            long ey = e[k] - e[i];

                            double val = ax * ay + bx * by + cx * cy + dx * dy + ex * ey;
                            long m1 = ax * ax + bx * bx + cx * cx + dx * dx + ex * ex;
                            long m2 = ay * ay + by * by + cy * cy + dy * dy + ey * ey;
                            val = val / Math.sqrt(m1);
                            val = val / Math.sqrt(m2);
                            if (Math.toDegrees(Math.acos(val)) + 0.000000001 < 90) {
                                bad.add(i);
                            }
                        }
                    }
                }

                out.println(n - bad.size());

                for (int i = 1; i <= n; i++) {
                    if (!bad.contains(i)) {
                        out.println(i);
                    }
                }
            }
        }

    }

    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());
        }

    }
}