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.
/*
ID: andrew42
LANG: JAVA
TASK: 
PROG: 
*/

import java.io.*;
import java.util.*;
import java.lang.*;

public class fived {
	static long[][] pts;
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		int numPts = input.nextInt();
		pts = new long[numPts][5];
		HashSet<Integer> works = new HashSet<Integer>();
		for (int i = 0; i < numPts; i++){
			works.add(i);
			for (int j = 0; j < 5; j++){
				pts[i][j] = input.nextLong();
			}
		}
		long[][] vects = new long[numPts][numPts];
		for (int i = 0; i < numPts; i++){
			for (int j = i+1; j < numPts; j++){
				long vect = 0;
				for (int m = 0; m < 5; m++){
					vect += (pts[j][m]-pts[i][m])*(pts[j][m]-pts[i][m]);
				}
				vects[i][j] = vects[j][i] = vect;
			}
		}
		ArrayList<Integer> cur = new ArrayList<Integer>();
		while (works.size() > 2){
			for (int i : works){
				cur.add(i);
				if (cur.size() == 3)
					break;
			}
			if (vects[cur.get(1)][cur.get(0)]+vects[cur.get(2)][cur.get(0)] > vects[cur.get(2)][cur.get(1)]){
				works.remove(cur.get(0));
				if (vects[cur.get(1)][cur.get(0)]+vects[cur.get(2)][cur.get(1)] > vects[cur.get(2)][cur.get(0)]){
					works.remove(cur.get(1));
					if (vects[cur.get(2)][cur.get(0)]+vects[cur.get(2)][cur.get(1)] > vects[cur.get(1)][cur.get(0)]){
						works.remove(cur.get(2));
					}
				} else {
					works.remove(cur.get(2));
				}
			} else {
				works.remove(cur.get(1)); works.remove(cur.get(2));
			}
			cur.clear();
		}
		for (int work : works){
			boolean bad = false;
			for (int i = 0; i < numPts; i++){
				for (int j = i+1; j < numPts; j++){
					if (vects[j][work]+vects[i][work] > vects[i][j]){
						bad = true; cur.add(work); break;
					}
				}
				if (bad)
					break;
			}
		}
		for (int i : cur)
			works.remove(i);
		System.out.println(works.size());
		for (int i : works){
			System.out.println(i+1);
		}
	}
}
