851_C. Five Dimensional Points_18759
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.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

/**
 * @author Don Li
 */
public class FiveDimensionalPoints {
    
    int MAX = 11;
    
    void solve() {
        int n = in.nextInt();
        int[][] x = new int[n][5];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < 5; j++) {
                x[i][j] = in.nextInt();
            }
        }
        
        if (n > MAX) {
            out.println(0);
            return;
        }
        
        List<Integer> res = new ArrayList<>();
        L:
        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;
                    if (acute(x[i], x[j], x[k])) {
                        continue L;
                    }
                }
            }
            res.add(i);
        }
        
        out.println(res.size());
        for (int i : res) out.println(i + 1);
    }
    
    boolean acute(int[] a, int[] b, int[] c) {
        int sum = 0;
        for (int i = 0; i < 5; i++) {
            sum += (b[i] - a[i]) * (c[i] - a[i]);
        }
        return sum > 0;
    }
    
    public static void main(String[] args) {
        in = new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
        out = new PrintWriter(System.out);
        new FiveDimensionalPoints().solve();
        out.close();
    }
    
    static FastScanner in;
    static PrintWriter out;
    
    static class FastScanner {
        BufferedReader in;
        StringTokenizer st;
        
        public FastScanner(BufferedReader in) {
            this.in = in;
        }
        
        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        
        public long nextLong() {
            return Long.parseLong(nextToken());
        }
        
        public double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}
