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.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Aeroui
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public int maxn = 1000 + 2;
        public int[] m = new int[maxn];
        int n;
        long[][] c = new long[maxn][6];

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            n = in.nextInt();
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < 5; ++j) {
                    c[i][j] = in.nextLong();
                }
            }

            Arrays.fill(m, (char) 0);
            for (int i = 0, flag = 0; i < n; ++i) {
                if (m[i] == 0) {
                    flag = 0;
                    for (int j = 0; j < n; ++j) {
                        if (j == i) continue;

                        for (int k = 0; k < n; ++k) {
                            if (j == k || k == i) continue;

                            if (dotProduct(i, j, k) <= 0) {
                                m[j] = m[k] = 1;
                            } else {
                                m[i] = 1;
                                flag = 1;
                                break;
                            }
                        }
                        if (flag != 0) break;
                    }
                }
            }

            int cnt = n;
            for (int i = 0; i < n; ++i)
                cnt -= m[i];

            out.println(cnt);
            for (int i = 0; i < n; ++i)
                if (m[i] == 0)
                    out.println(i + 1);
        }

        public long dotProduct(int i, int j, int k) {
            long ret = 0;
            for (int cd = 0; cd < 5; ++cd)
                ret += (c[k][cd] - c[i][cd]) * (c[j][cd] - c[i][cd]);
            return ret;
        }

    }
}

