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.Scanner;

public class P851C
{
	static double eps = 1e-9;
	public static void main(String[] args)
	{
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		if (n > 11)
		{
			System.out.println(0);
			return;
		}
		int[][] arr = new int[n][5];
		for (int i = 0; i < n; i++)
		{
			for (int j = 0; j < 5; j++)
			{
				arr[i][j] = scan.nextInt();
			}
		}
		ArrayList<Integer> list = new ArrayList<>();
		for (int i = 0; i < n; i++)
		{
			boolean good = true;
			Loop:
			for (int j = 0; j < n; j++)
			{
				if (j == i)
					continue;
				for (int k = j+1; k < n; k++)
				{
					if (k == i)
						continue;
					Vector v1 = new Vector(arr[i], arr[j]);
					Vector v2 = new Vector(arr[i], arr[k]);
					double angle = Math.acos(v1.prod(v2)/(v1.mag()*v2.mag()));
					if (angle < Math.PI/2-eps)
					{
						good = false;
						break Loop;
					}
				}
			}
			if (good)
				list.add(i+1);
		}
		System.out.println(list.size());
		for (int i : list)
			System.out.println(i);
	}
	static class Vector
	{
		int[] arr = new int[5];
		Vector(int[] a, int[] b)
		{
			for (int i = 0; i < 5; i++)
			{
				arr[i] = b[i]-a[i];
			}
		}
		double mag()
		{
			double sum = 0;
			for (int i = 0; i < arr.length; i++)
			{
				sum += arr[i]*arr[i];
			}
			return Math.sqrt(sum);
		}
		int prod(Vector v)
		{
			int sum = 0;
			for (int i = 0; i < arr.length; i++)
			{
				sum += arr[i]*v.arr[i];
			}
			return sum;
		}
	}
}
