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.IOException;
import java.io.PrintWriter;
import java.util.*;
import java.io.*;

public class Main {
    public class point {
        int a[];

        point(int x, int y, int z, int t, int l) {
            a = new int[5];
            a[0] = x;
            a[1] = y;
            a[2] = z;
            a[3] = t;
            a[4] = l;
        }
    }

    point raz(point a, point b) {
        int[] x = a.a;
        int[] y = b.a;
        return new point(x[0] - y[0], x[1] - y[1], x[2] - y[2], x[3] - y[3], x[4] - y[4]);
    }

    boolean len(point a, point b) {
        int z = 0;
        for (int i = 0; i < 5; i++) {
            z += a.a[i] * b.a[i];
        }
        if (z > 0) {
            return false;
        }
        return true;
    }

    boolean ugl(point a, point b, point c) {
        return len(raz(b, a), raz(c, a));
    }

    public void solve() throws IOException {
        int n = nextInt();
        if (n > 2) {
            point[] a = new point[n];
            for (int i = 0; i < n; i++) {
                a[i] = new point(nextInt(), nextInt(), nextInt(), nextInt(), nextInt());
            }
            Stack<Integer> q = new Stack<>();
            for (int i = 0; i < n; i++) {
                q.add(i);
            }
            while (q.size() > 2) {
                int z1 = q.pop();
                int z2 = q.pop();
                int z3 = q.pop();
                if (ugl(a[z1], a[z2], a[z3])) {
                    q.add(z1);
                }
                if (ugl(a[z2], a[z1], a[z3])) {
                    q.add(z2);
                }
                if (ugl(a[z3], a[z2], a[z1])) {
                    q.add(z3);
                }
            }
            int z = 0;
            if (q.size() == 0) {
                out.print(0);
            } else {
                while (q.size() > 0) {
                    boolean t = true;
                    int x = q.pop();
                    for (int i = 0; i < n; i++) {
                        for (int j = 0; j < n; j++) {
                            if (i != j && x != i && x != j) {
                                if (!ugl(a[x], a[i], a[j])) {
                                    t = false;
                                }
                            }
                        }
                    }
                    if (t) {
                        z++;
                        out.println(1);
                        out.print(x + 1);
                    }
                }
                if(z == 0){
                    out.print(0);
                }
            }
        } else {
            out.println(n);
            for(int i = 0; i < n; i++){
                out.println((i + 1));
            }
        }
    }


    BufferedReader br;
    StringTokenizer sc;
    PrintWriter out;

    public String nextToken() throws IOException {
        while (sc == null || !sc.hasMoreTokens()) {
            try {
                sc = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                return null;
            }
        }
        return sc.nextToken();
    }

    public boolean hasNext() throws IOException {
        while (sc == null || !sc.hasMoreTokens()) {
            try {
                sc = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                return false;
            }
        }
        return true;
    }

    public Integer nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public Long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public Double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public static void main(String[] args) throws IOException {
        try {
            Locale.setDefault(Locale.US);
        } catch (Exception e) {
        }
        new Main().run();
    }

    public void run() {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
//            br = new BufferedReader(new FileReader("a"));
//            out = new PrintWriter(new File("a"));
            solve();
            out.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }
}