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.*;
import java.util.*;

public class C {
	public static void main(String[] args) throws IOException {
        BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer tokenizer = new StringTokenizer(input.readLine());
		StringBuilder output = new StringBuilder();
		String newLine = System.lineSeparator();

		int n = Integer.parseInt(tokenizer.nextToken());
		P[] pts = new P[n];
		boolean[] bad = new boolean[n];

		for (int i = 0; i < n; i++) {
			tokenizer = new StringTokenizer(input.readLine());
			long a = Long.parseLong(tokenizer.nextToken());
			long b = Long.parseLong(tokenizer.nextToken());
			long c = Long.parseLong(tokenizer.nextToken());
			long d = Long.parseLong(tokenizer.nextToken());
			long e = Long.parseLong(tokenizer.nextToken());
			pts[i] = new P(a, b, c, d, e);
		}

		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n && !bad[i]; j++) {
				if (i != j) {
					for (int k = 0; k < n && !bad[i]; k++) {
						if (j != k && i != k) {
							long dot = pts[j].sub(pts[i]).dot(pts[k].sub(pts[i]));
							// System.err.println((i + 1) + ", " + (j + 1) + ", " + (k + 1) + ": " + dot);
							if (dot > 0) {
								bad[i] = true;
							} else {
								bad[j] = true;
								bad[k] = true;
							}
							// System.err.println(Arrays.toString(bad));
						}
					}
				}
			}
		}

		int count = 0;
		for (int i = 0; i < n; i++) {
			if (!bad[i]) {
				count++;
				output.append(i + 1);
				output.append(newLine);
			}
		}

		System.out.println(count);
		System.out.print(output.toString());
	}
	static class P {
		final long a, b, c, d, e;
		P(long a, long b, long c, long d, long e)    { this.a = a; this.b = b; this.c = c; this.d = d; this.e = e; }
		P sub(P that)            { return new P(a - that.a, b - that.b, c - that.c, d - that.d, e - that.e); }
		long dot(P that)       { return a * that.a + b * that.b + c * that.c + d * that.d + e * that.e; }
	}
}
