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.Arrays;
import java.util.InputMismatchException;
import java.io.IOException;
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 {
        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[] good = new boolean[n];
            Arrays.fill(good, true);
            externalLoop:
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (i != j) {
                        for (int k = 0; k < n; k++) {
                            if (j != k && k != i) {
                                if (points[i].isNotGood(points[j], points[k])) {
                                    good[i] = false;
                                    continue externalLoop;
                                } else {
                                    good[j] = good[k] = false;
                                }
                            }
                        }
                    }
                }
            }
            int ans = 0;
            for (int i = 0; i < n; i++) {
                ans += good[i] ? 1 : 0;
            }
            out.println(ans);
            for (int i = 0; i < n; i++) {
                if (good[i]) {
                    out.println(i + 1);
                }
            }
        }

    }

    static class InputReader {
        private int lenbuf = 0;
        private int ptrbuf = 0;
        private InputStream in;
        private byte[] inbuf = new byte[1024];

        public InputReader(InputStream in) {
            this.in = in;
        }

        private int readByte() {
            if (lenbuf == -1) throw new InputMismatchException();
            if (ptrbuf >= lenbuf) {
                ptrbuf = 0;
                try {
                    lenbuf = in.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0) return -1;
            }
            return inbuf[ptrbuf++];
        }

        public int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

    }

    static class Point {
        int x1;
        int x2;
        int x3;
        int x4;
        int x5;

        Point(int x1, int x2, int x3, int x4, int x5) {
            this.x1 = x1;
            this.x2 = x2;
            this.x3 = x3;
            this.x4 = x4;
            this.x5 = x5;
        }

        long scalar(Point p) {
            return x1 * p.x1 + x2 * p.x2 + x3 * p.x3 + x4 * p.x4 + x5 * p.x5;
        }

        boolean isNotGood(Point p1, Point p2) {
            Point a = new Point(p1.x1 - x1, p1.x2 - x2, p1.x3 - x3, p1.x4 - x4, p1.x5 - x5);
            Point b = new Point(p2.x1 - x1, p2.x2 - x2, p2.x3 - x3, p2.x4 - x4, p2.x5 - x5);
            return a.scalar(b) > 0;
        }

    }
}

