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 javax.swing.plaf.basic.BasicButtonUI;
import java.io.*;
import java.util.ArrayList;
import java.util.StringTokenizer;

/**
 * Created by dell on 2017/9/6.
 */
public class C {

    private int n;
    private int[][] pt = new int[1000][5];

    public void read() throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());

        n = Integer.parseInt(st.nextToken());
        for (int i = 0; i < n; i++) {
            st = new StringTokenizer(br.readLine());
            for (int j=0;j<5;j++)
                pt[i][j] = Integer.parseInt(st.nextToken());
        }

        br.close();
    }

    private boolean jug(int a) {

        for (int b=0;b<n;b++) {
            if (b == a) continue;
            for (int c=b+1;c<n;c++) {
                if (c == a) continue;

                long bc = 0;
                for (int i=0;i<5;i++) {
                    bc += (pt[b][i]-pt[a][i]) * (pt[c][i]-pt[a][i]);
                }

                if (bc > 0) return false;
            }
        }

        return true;
    }

    public void run() throws IOException {

        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        read();

        if (n > 11) {
            bw.write("0");
        } else {
            ArrayList lst = new ArrayList();
            for (int i = 0;i<n;i++)
                if (jug(i) == true) {
                    lst.add(i+1);
                }

            bw.write(String.valueOf(lst.size()));
            for (Object i : lst) {
                bw.newLine();
                bw.write(i.toString());
            }
        }

        bw.flush();
        bw.close();
    }

    public static void main(String[] args) throws IOException {
        C c = new C();
        c.run();
    }
}