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.util.*;
import java.io.*;
import java.math.*;
import java.util.regex.*;

public class Main {

    static Scanner input = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
    static Reader fastInput = new Reader();

    public static void main(String[] args) throws IOException {
        int n = fastInput.nextInt();
        if (n > 20) {
            System.out.println(0);
        } else {
            int[][] p = new int[n][5];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < 5; j++) {
                    p[i][j] = fastInput.nextInt();
                }
            }
            ArrayList<Integer> good = new ArrayList<>();
            loop:
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (i != j) {
                        for (int k = j + 1; k < n; k++) {
                            if (i != k) {
                                if (getAn(p[i], p[j], p[k]) < 90) {
                                    continue loop;
                                }
                            }
                        }
                    }
                }
                good.add(i + 1);
            }
            System.out.println(good.size());
            for (int i = 0; i < good.size(); i++) {
                System.out.println(good.get(i));
            }
        }
    }

    static double getAn(int[] p1, int[] p2, int[] p3) {
        double dot = 0, aLen = 0, bLen = 0;
        for (int i = 0; i < p1.length; i++) {
            dot += (p2[i] - p1[i]) * (p3[i] - p1[i]);
            aLen += (p2[i] - p1[i]) * (p2[i] - p1[i]);
            bLen += (p3[i] - p1[i]) * (p3[i] - p1[i]);
        }
        return 180 * Math.acos(dot / Math.sqrt(aLen * bLen)) / Math.PI;
    }

    static class Reader {

        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') {
                    break;
                }
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean neg = (c == '-');
            if (neg) {
                c = read();
            }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg) {
                return -ret;
            }
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean neg = (c == '-');
            if (neg) {
                c = read();
            }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) {
                return -ret;
            }
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean neg = (c == '-');
            if (neg) {
                c = read();
            }

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg) {
                return -ret;
            }
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) {
                buffer[0] = -1;
            }
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) {
                fillBuffer();
            }
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null) {
                return;
            }
            din.close();
        }
    }
}