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.util.*;
import java.io.*;
public class C {
  public static void main(String[] args) {
    Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
    int n = in.nextInt();
    int[][] pts= new int[n][5];
    boolean[] good = new boolean[n];
    for (int i = 0; i < n; i++) {
      good[i] = true;
      for (int j = 0; j < 5; j++) {
        pts[i][j] = in.nextInt();
      }
    }
    int count = 0;
    outer: for (int i = 0; i < n; i++) {
      if (!good[i])
        continue;
      for (int j = 0; j < n; j++) {
        if (j == i)
          continue;
        for (int k = 0; k < n; k++) {
          if (k == i || k == j)
            continue;
          int inpd = 0;
          for (int l = 0; l < 5; l++) {
            inpd += (pts[k][l]-pts[i][l])*(pts[j][l]-pts[i][l]);
          }
          if (inpd > 0) { //acute
            good[i] = false;
            continue outer;
          } else { //obtuse
            good[j] = false;
            good[k] = false;
          }
        }
      }
      count++;
    }
    System.out.println(count);
    for (int i = 0; i < n; i++) {
      if (good[i])
        System.out.println(i+1);
    }
    in.close();
  }
}