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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;

public class C {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int[][] points = new int[n][5];
		for (int i = 0; i < n; i++) {
			String[] arr = br.readLine().split(" ");
			for (int j = 0; j < 5; j++) {
				points[i][j] = Integer.parseInt(arr[j]);
			}
		}
		List<Integer> good = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			boolean bad = false;
			for (int j = 0; !bad && j < n; j++) {
				for (int k = 0; !bad && k < n; k++) {
					if (i == j || j == k || i == k) { continue; }
					int[] midpoint = points[i];
					int[] point1 = new int[5];
					int[] point2 = new int[5];
					for (int x = 0; x < 5; x++) {
						point1[x] = points[j][x] - midpoint[x];
						point2[x] = points[k][x] - midpoint[x];
					}
					int res = dot(point1, point2);
					if (res > 0) {
						bad = true;
					}
				}
			}
			if (!bad) {
				good.add(i);
			}
		}
		System.out.println(good.size());
		for (int i : good) {
			System.out.println(i + 1);
		}
	}
	
	public static int dot(int[] v1, int[] v2) {
		return v1[0] * v2[0] +
				v1[1] * v2[1] +
				v1[2] * v2[2] +
				v1[3] * v2[3] +
				v1[4] * v2[4];
	}

}
