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.PriorityQueue;
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;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        C851 solver = new C851();
        solver.solve(1, in, out);
        out.close();
    }

    static class C851 {
        int MAGIC = 100;
        int N;
        Point[] points;

        boolean ok(int q) {
            for (int i = 0; i < N; i++) {
                if (i == q) continue;
                for (int j = 0; j < N; j++) {
                    if (j == q || j == i) continue;
                    if (points[q].vec(points[i]).abt(points[q].vec(points[j])) < 90) {
//                    System.out.printf("Point %d is bad due to points %d and %d (angle %f)%n", q, i, j, points[q].vec(points[i]).abt(points[q].vec(points[j])));
                        return false;
                    }
                }
            }
            return true;
        }

        public void solve(int testNumber, FastScanner s, PrintWriter out) {

            N = s.nextInt();
            if (N > MAGIC) {
                out.println(0);
                return;
            }

            points = new Point[N];
            for (int i = 0; i < N; i++) {
                points[i] = new Point(s.nextInt(), s.nextInt(), s.nextInt(), s.nextInt(), s.nextInt());
            }

            PriorityQueue<Integer> neato = new PriorityQueue<>();
            for (int i = 0; i < N; i++) {
                if (ok(i)) {
                    neato.add(i + 1);
                }
            }

            out.println(neato.size());
            while (neato.size() > 0)
                out.println(neato.poll());

        }

        class Point {
            int a;
            int b;
            int c;
            int d;
            int e;

            public Point(int A, int B, int C, int D, int E) {
                a = A;
                b = B;
                c = C;
                d = D;
                e = E;
            }

            Vector vec(Point P) {
                return new Vector(P.a - a, P.b - b, P.c - c, P.d - d, P.e - e);
            }

        }

        class Vector {
            int a;
            int b;
            int c;
            int d;
            int e;
            double mag;

            public Vector(int A, int B, int C, int D, int E) {
                a = A;
                b = B;
                c = C;
                d = D;
                e = E;
                mag = Math.sqrt(a * a + b * b + c * c + d * d + e * e);
            }

            int dot(Vector V) {
                return a * V.a + b * V.b + c * V.c + d * V.d + e * V.e;
            }

            double abt(Vector V) {
                return Math.acos(dot(V) / (mag * V.mag)) * 180.0 / Math.PI;
            }

        }

    }

    static class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public FastScanner(InputStream stream) {
            this.stream = stream;
        }

        int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

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

        public String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

    }
}

