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;
int main() {
  int n;
  cin >> n;
  std::vector<int> v;
  double a[n][5];
  for (int i = (0); i < (n); i++) {
    for (int j = (0); j < (5); j++) {
      cin >> a[i][j];
    }
  }
  int s, flag;
  for (int i = (0); i < (n); i++) {
    flag = 0;
    for (int j = (0); j < (i); j++) {
      for (int k = (j + 1); k < (i); k++) {
        s = 0;
        for (int m = (0); m < (5); m++) {
          s += (a[j][m] - a[i][m]) * (a[k][m] - a[i][m]);
        }
        if (s > 0) {
          flag = 1;
          goto brk;
        }
      }
      for (int k = (i + 1); k < (n); k++) {
        s = 0;
        for (int m = (0); m < (5); m++) {
          s += (a[j][m] - a[i][m]) * (a[k][m] - a[i][m]);
        }
        if (s > 0) {
          flag = 1;
          goto brk;
        }
      }
    }
    for (int j = (i + 1); j < (n); j++) {
      for (int k = (j + 1); k < (n); k++) {
        s = 0;
        for (int m = (0); m < (5); m++) {
          s += (a[j][m] - a[i][m]) * (a[k][m] - a[i][m]);
        }
        if (s > 0) {
          flag = 1;
          goto brk;
        }
      }
    }
  brk:
    if (flag == 0) v.push_back(i);
  }
  int size = v.size();
  cout << size << "\n";
  for (int i = (0); i < (size); i++) {
    cout << v[i] + 1 << "\n";
  }
  return 0;
}
