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 Main {
	InputReader scn;
	PrintWriter out;
	String INPUT = "";

	class point {
		long[] pnt = new long[5];
		int ind;

		point(int... arr) {
			for (int i = 0; i < 5; i++) {
				pnt[i] = arr[i];
			}
		}

		point(){}
		
		long dist() {
			long d = 0;
			for(int i = 0; i < 5; i++) {
				d += pnt[i] * pnt[i];
			}
			return d;
		}
		
		double scalar(point p) {
			long d = 0;
			for(int i = 0; i < 5; i++) {
				d += this.pnt[i] * p.pnt[i];
			}
			if(this.dist() == 0 || p.dist() == 0) {
				return 90.0;
			}
			double cos =  d / Math.sqrt(this.dist() * p.dist());
			return Math.toDegrees(Math.abs(Math.acos(cos)));
		}
		
		point vec(point p) {
			point rv = new point();
			for(int i = 0; i < 5; i++) {
				rv.pnt[i] = this.pnt[i] - p.pnt[i];
			}
			return rv;
		}
	}

	void solve() {
		int n = scn.nextInt();
		point[] arr = new point[n];
		for (int i = 0; i < n; i++) {
			arr[i] = new point(scn.nextArray(5));
			arr[i].ind = i;
		}

		Random r = new Random();
		boolean[] good = new boolean[n];
		Arrays.fill(good, true);
		for(int i = 0; i < n; i++) {
			for(int j = 0; j < n && good[i]; j++) {
				if(i == j) {
					continue;
				}
				point u = arr[i].vec(arr[j]);
				for(int k = r.nextInt(n), z = 0; z < n && good[i]; k = (k + 1) % n, z++) {
					if(i == k || j == k) {
						continue;
					}
					point v = arr[i].vec(arr[k]);
					if(u.scalar(v) < 90) {
						good[i] = false;
					}
				}
			}
		}
		
		int k = 0;
		for(int i = 0; i < n; i++) {
			if(good[i]) {
				out.print(i + 1 + " ");
				k++;
			}
		}
		System.out.println(k);
	}

	long gcd(long a, long b) {
		return b == 0 ? a : gcd(b, a % b);
	}

	void run() throws Exception {
		boolean onlineJudge = System.getProperty("ONLINE_JUDGE") != null;
		out = new PrintWriter(System.out);
		scn = new InputReader(onlineJudge);
		long time = System.currentTimeMillis();
		solve();
		out.flush();
		if (!onlineJudge) {
			System.out.println(Arrays.deepToString(new Object[] { System.currentTimeMillis() - time + " ms" }));
		}
	}

	public static void main(String[] args) throws Exception {
		new Main().run();
	}

	class InputReader {
		InputStream is;

		public InputReader(boolean onlineJudge) {
			is = onlineJudge ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		}

		byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;

		int readByte() {
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) {
				ptrbuf = 0;
				try {
					lenbuf = is.read(inbuf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}

		boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		char nextChar() {
			return (char) skip();
		}

		String next() {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		char[] next(int n) {
			char[] buf = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) {
				buf[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buf : Arrays.copyOf(buf, p);
		}

		char[][] nextMatrix(int n, int m) {
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = next(m);
			return map;
		}

		int[] nextArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		int nextInt() {
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}

			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}

		long nextLong() {
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}

			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	}
}