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.
#include <bits/stdc++.h>
using namespace std;
double angle(int vector1[], int vector2[]) {
  double num = 0;
  for (int i = 0; i < 5; i++) {
    num += (vector1[i] * vector2[i]);
  }
  double den = 1;
  double temp = 0;
  for (int i = 0; i < 5; i++) temp += vector1[i] * vector1[i];
  den *= sqrt(temp);
  temp = 0;
  for (int i = 0; i < 5; i++) temp += vector2[i] * vector2[i];
  den *= sqrt(temp);
  return num / den;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  cin >> n;
  int points[n][5];
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < 5; j++) cin >> points[i][j];
  }
  bool bad[n];
  for (int i = 0; i < n; i++) bad[i] = false;
  int vector1[5], vector2[5];
  for (int i = 0; i < n; i++) {
    if (bad[i]) break;
    for (int j = 0; j < n; j++) {
      if (bad[i]) break;
      if (i == j)
        continue;
      else {
        for (int k = 0; k < n; k++) {
          if (k == j)
            continue;
          else {
            for (int l = 0; l < 5; l++)
              vector1[l] = points[k][l] - points[i][l];
            for (int l = 0; l < 5; l++)
              vector2[l] = points[j][l] - points[i][l];
            if (angle(vector1, vector2) > 0) {
              bad[i] = true;
              break;
            }
          }
        }
      }
    }
  }
  long long counter = 0;
  for (int i = 0; i < n; i++) {
    if (!bad[i]) counter++;
  }
  cout << counter << "\n";
  if (counter == 0) return 0;
  for (int i = 0; i < n; i++) {
    if (!bad[i]) cout << i + 1 << " ";
  }
  cout << "\n";
  return 0;
}
