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.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.util.ArrayList;
import java.util.List;

public class C {

    static PrintWriter out = new PrintWriter(System.out);
    static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));


    public static void main(String[] args) throws Exception{
        long[][] coo = new long[1010][5];
        int n = Integer.valueOf(reader.readLine());
        for (int i = 0; i < n; i++) {
            String[] ar = reader.readLine().split(" ");
            for (int j = 0; j < 5; j++) {
                coo[i][j] = Long.valueOf(ar[j]);
            }
        }

        if (n > 32) {
            System.out.println(0);
            return;
        }

        List<Integer> ret = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            if (check(i, n, coo)){
                ret.add(i + 1);
            }
        }
        System.out.println(ret.size());
        ret.forEach(out::println);
        out.flush();
    }

    static boolean check(int ith, int n, long[][] coo){
        for (int i = 0; i < n; i++) {
            if (i == ith) continue;
            for (int j = 0; j < n; j++) {
                if (j == i || j == ith) continue;
                if (!isAcute(ith, i, j, coo)) return false;
            }
        }
        return true;
    }

    static boolean isAcute(int a, int b, int c, long[][] coo){
        long sum = 0;
        for (int i = 0; i < 5; i++) {
            sum += (coo[b][i] - coo[a][i]) * (coo[c][i] - coo[a][i]);
        }
        if (sum > 0) return false;
        return true;
    }
}

