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.Scanner;

public class C851FiveDimensionalPoints {

	public static class Vector {
		public int a,b,c,d,e;
		public Vector(int a, int b, int c, int d, int e) {
			this.a = a; this.b = b; this.c = c; this.d = d; this.e = e;
		}
		public Vector(FPoint a, FPoint b) {
			this.a = b.a - a.a;
			this.b = b.b - a.b;
			this.c = b.c - a.c;
			this.d = b.d - a.d;
			this.e = b.e - a.e;
		}
		public double angle(Vector v) {
			return Math.acos(prod(v) / (v.magnitude() * this.magnitude()));
		}
		public double prod(Vector v) {
			return a * v.a + b * v.b + c * v.c + d * v.d + e * v.e;
		}
		public double magnitude() {
			return prod(this);
		}
	}
	
	public static class FPoint {
		public int a,b,c,d,e;
		public FPoint(int a, int b, int c, int d, int e) {
			this.a = a; this.b = b; this.c = c; this.d = d; this.e = e;
		}
	}
	
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		FPoint[] ar = new FPoint[n];
		for (int i = 0; i < n; i++) {
			ar[i] = new FPoint(in.nextInt(), in.nextInt(), in.nextInt(), in.nextInt(), in.nextInt());
		}
		boolean[] good = new boolean[n];
		int ans = 0;
main:	for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				if (j == i) {
					continue;
				}
				for (int k = 0; k < n; k++) {
					if (k == i || k == j) {
						continue;
					}
					Vector a = new Vector(ar[i], ar[j]);
					Vector b = new Vector(ar[i], ar[k]);
//					System.out.println(a.angle(b));
					if (a.angle(b) < Math.PI / 2) {
						continue main;
					}
				}
			}
			good[i] = true;
			ans++;
		}
		
		System.out.println(ans);
		for (int i = 0; i < n; i++) {
			if (good[i]) {
				System.out.println(i + 1);
			}
		}
		 
	}
	
}
