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.List;
import java.util.StringTokenizer;
import java.io.IOException;
import java.util.InputMismatchException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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 {
        int[] a;
        int[] b;
        int[] c;
        int[] d;
        int[] e;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            a = new int[n];
            b = new int[n];
            c = new int[n];
            d = new int[n];
            e = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
                b[i] = in.nextInt();
                c[i] = in.nextInt();
                d[i] = in.nextInt();
                e[i] = in.nextInt();
            }

            if (n == 1) {
                out.println(1);
                out.println(1);
                return;
            }

            if (n == 2) {
                out.println(2);
                out.println(1);
                out.println(2);
                return;
            }

            if (n > 11) {
                out.println(0);
                return;
            }

            List<Integer> list = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                boolean flg = true;
                out:
                for (int j = 0; j < n; j++) {
                    for (int k = 0; k < n; k++) {
                        if (i == j || j == k || k == i) continue;

                        if ((a[j] - a[i]) * (a[k] - a[i]) + (b[j] - b[i]) * (b[k] - b[i]) + (c[j] - c[i]) * (c[k] - c[i]) + (d[j] - d[i]) * (d[k] - d[i]) + (e[j] - e[i]) * (e[k] - e[i]) > 0) {
                            flg = false;
                            break out;
                        }
                    }
                }
                if (flg) list.add(i + 1);
            }

            out.println(list.size());
            for (int x : list) {
                out.println(x);
            }
        }

    }

    static class InputReader {
        BufferedReader in;
        StringTokenizer tok;

        public String nextString() {
            while (!tok.hasMoreTokens()) {
                try {
                    tok = new StringTokenizer(in.readLine(), " ");
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
            }
            return tok.nextToken();
        }

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

        public InputReader(InputStream inputStream) {
            in = new BufferedReader(new InputStreamReader(inputStream));
            tok = new StringTokenizer("");
        }

    }
}

