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.*;

public class Main {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();

        List<Point> points = new ArrayList<Point>(n);
        for (int i = 0; i < n; i++) {
            Point point = new Point();
            point.p1 = in.nextInt();
            point.p2 = in.nextInt();
            point.p3 = in.nextInt();
            point.p4 = in.nextInt();
            point.p5 = in.nextInt();
            points.add(point);
        }

        List<Integer> indexes = new ArrayList<Integer>(n);
        for (int i = 0; i < n; i++) {
            Point a = points.get(i);
            boolean bed = false;
            for (int j = 0; j < n; j++) {
                if (j == i) continue;
                Point b = points.get(j);
                for (int k = 0; k < n; k++) {
                    if (k == i || k == j) continue;
                    Point c = points.get(k);
                    Vector ab = new Vector(a, b);
                    Vector ac = new Vector(a, c);
                    if(Vector.arccos(ab, ac) < 90.0){
                        bed = true;
                        break;
                    }
                }
                if (bed) break;
            }
            if(!bed) indexes.add(i + 1);
        }

        p(indexes.size());
        pl(indexes);
    }

    static void p(Object str) {
        System.out.println(str);
    }

    static class Point {
        int p1;
        int p2;
        int p3;
        int p4;
        int p5;
    }

    static class Vector {
        int p1;
        int p2;
        int p3;
        int p4;
        int p5;

        Vector(Point p1, Point p2) {
            this.p1 = p2.p1 - p1.p1;
            this.p2 = p2.p2 - p1.p2;
            this.p3 = p2.p3 - p1.p3;
            this.p4 = p2.p4 - p1.p4;
            this.p5 = p2.p5 - p1.p5;
        }

        static int scal(Vector v1, Vector v2) {
            return v1.p1 * v2.p1 + v1.p2 * v2.p2 + v1.p3 * v2.p3 + v1.p4 * v2.p4 + v1.p5 * v2.p5;
        }

        double mod() {
            return Math.sqrt(scal(this, this));
        }

        static double arccos(Vector v1, Vector v2) {
            return Math.acos(scal(v1, v2) / (v1.mod() * v2.mod())) * 180 / Math.PI;
        }
    }

    public static void pa(int[] objs) {
        String str = "";
        for (Object obj : objs) {
            str += obj.toString() + " ";
        }
        p(str);
    }

    public static void pi(Object[] objs) {
        String str = "";
        for (Object obj : objs) {
            str += obj.toString() + " ";
        }
        p(str);
    }

    public static void pl(List<Integer> objs) {
        String str = "";
        for (Integer obj : objs) {
            str += obj + " ";
        }
        p(str);
    }

}

