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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

/**
 * Created by igarus on 17.10.2016.
 */
public class CF_432_C {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int n = scanner.nextInt();

        int[][] x = new int[n][5];

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < 5; j++)
                x[i][j] = scanner.nextInt();
        }
        ArrayList<Integer> ids = new ArrayList<>();
        boolean isBreak;

        for (int i = 0; i < n; i++) {
            int[] a = x[i];
            isBreak = false;
            for (int j = 0; j < n; j++) {
                if (i != j) {
                    int[] b = x[j];
                    for (int k = 0; k < n; k++) {
                        int[] c = x[k];
                        if (i != k && j != k) {
                            int[] ab = new int[]{b[0] - a[0], b[1] - a[1], b[2] - a[2], b[3] - a[3], b[4] - a[4]};
                            int[] ac = new int[]{c[0] - a[0], c[1] - a[1], c[2] - a[2], c[3] - a[3], c[4] - a[4]};
                            int s = ab[0] * ac[0] + ab[1] * ac[1] + ab[2] * ac[2] + ab[3] * ac[3] + ab[4] * ac[4];
                            double db = Math.sqrt(ab[0] * ab[0] + ab[1] * ab[1] + ab[2] * ab[2] + ab[3] * ab[3] + ab[4] * ab[4]);
                            double dc = Math.sqrt(ac[0] * ac[0] + ac[1] * ac[1] + ac[2] * ac[2] + ac[3] * ac[3] + ac[4] * ac[4]);
                            double angle = Math.acos(s / (db * dc));
                            //System.out.println(i + ") [" + j + ":" + k + "] angle = " + angle);
                            if (angle < Math.PI / 2) {
                                isBreak = true;
                                break;
                            }
                        }
                    }
                }
                if (isBreak)
                    break;
            }
            if (!isBreak)
                ids.add(i);
        }
        System.out.println(ids.size());
        for (int id : ids)
            System.out.println(id + 1);

    }

    public static void print(int[] point) {
        System.out.println(Arrays.toString(point));
    }

}
